121 relations: Acoustics, Adomian decomposition method, Aleksandr Lyapunov, Analytic function, Ansatz, Bäcklund transform, Boundary (topology), Boundary value problem, Cauchy problem, Cauchy–Kowalevski theorem, Change of variables (PDE), Classical electromagnetism, Computer, Computer simulation, Configuration space (physics), Conic section, Constant (mathematics), Contact geometry, Continuous or discrete variable, Convolution, Del, Derivative, Diagonal matrix, Differential equation, Differential geometry, Dirichlet boundary condition, Discontinuous Galerkin method, Discriminant, Divergence theorem, Dynamical system, Eigenvalues and eigenvectors, Elasticity (physics), Electrostatics, Elliptic partial differential equation, Euler–Tricomi equation, Extended finite element method, Finite difference, Finite difference method, Finite element method, Finite volume method, Fluid, Fluid dynamics, Fourier analysis, Fourier series, Fourier transform, Function (mathematics), Fundamental solution, Green's function, Group theory, Heat, ..., Heat equation, Heat transfer, Helmholtz equation, Homogeneous polynomial, Homotopy analysis method, Homotopy principle, Hp-FEM, Hyperbolic partial differential equation, Impulse response, Infinitesimal transformation, Integral transform, Jet bundle, Klein–Gordon equation, Laplace operator, Laplace transform applied to differential equations, Laplace's equation, Lax pair, Lewy's example, Lie algebra, Lie group, Lie theory, Linear function, List of dynamical systems and differential equations topics, Logical consequence, Mathematical analysis, Mathematics, Matrix differential equation, Meshfree methods, Method of characteristics, Method of quantum characteristics, Multidimensional system, Multigrid method, Multivariable calculus, Neumann boundary condition, Nonlinear Schrödinger equation, Numerical analysis, Numerical partial differential equations, Ordinary differential equation, Overdetermined system, Parabolic partial differential equation, Partial derivative, Partial differential algebraic equation, Perturbation theory, Phase space formulation, Picard–Lindelöf theorem, Poisson's equation, Pressure, Probability distribution, Quadratic form, Quantum mechanics, Recurrence relation, Rigid body, Robin boundary condition, Separable partial differential equation, Signal processing, Sophus Lie, Sound, Spectral element method, Split-step method, Stochastic partial differential equation, Stochastic processes and boundary value problems, Supercomputer, Superposition principle, Temperature, Underdetermined system, Uniform convergence, Uniqueness quantification, Wave equation, Weak solution, Well-posed problem, Wigner quasiprobability distribution. Expand index (71 more) »
Acoustics
Acoustics is the branch of physics that deals with the study of all mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound.
New!!: Partial differential equation and Acoustics · See more »
Adomian decomposition method
The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations.
New!!: Partial differential equation and Adomian decomposition method · See more »
Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov (Алекса́ндр Миха́йлович Ляпуно́в,; – November 3, 1918) was a Russian mathematician, mechanician and physicist.
New!!: Partial differential equation and Aleksandr Lyapunov · See more »
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
New!!: Partial differential equation and Analytic function · See more »
Ansatz
In physics and mathematics, an ansatz (meaning: "initial placement of a tool at a work piece", plural ansätze; or ansatzes) is an educated guessIn his book on "The Nature of Mathematical Modelling", Neil Gershenfeld introduces ansatz, with interpretation "a trial answer", to be an important technique for solving differential equations.
New!!: Partial differential equation and Ansatz · See more »
Bäcklund transform
In mathematics, Bäcklund transforms or Bäcklund transformations (named after the Swedish mathematician Albert Victor Bäcklund) relate partial differential equations and their solutions.
New!!: Partial differential equation and Bäcklund transform · See more »
Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.
New!!: Partial differential equation and Boundary (topology) · See more »
Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
New!!: Partial differential equation and Boundary value problem · See more »
Cauchy problem
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain.
New!!: Partial differential equation and Cauchy problem · See more »
Cauchy–Kowalevski theorem
In mathematics, the Cauchy–Kowalevski theorem (also written as the Cauchy–Kovalevskaya theorem) is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems.
New!!: Partial differential equation and Cauchy–Kowalevski theorem · See more »
Change of variables (PDE)
Often a partial differential equation can be reduced to a simpler form with a known solution by a suitable change of variables.
New!!: Partial differential equation and Change of variables (PDE) · See more »
Classical electromagnetism
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.
New!!: Partial differential equation and Classical electromagnetism · See more »
Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
New!!: Partial differential equation and Computer · See more »
Computer simulation
Computer simulation is the reproduction of the behavior of a system using a computer to simulate the outcomes of a mathematical model associated with said system.
New!!: Partial differential equation and Computer simulation · See more »
Configuration space (physics)
In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system.
New!!: Partial differential equation and Configuration space (physics) · See more »
Conic section
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.
New!!: Partial differential equation and Conic section · See more »
Constant (mathematics)
In mathematics, the adjective constant means non-varying.
New!!: Partial differential equation and Constant (mathematics) · See more »
Contact geometry
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'.
New!!: Partial differential equation and Contact geometry · See more »
Continuous or discrete variable
In mathematics, a variable may be continuous or discrete.
New!!: Partial differential equation and Continuous or discrete variable · See more »
Convolution
In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
New!!: Partial differential equation and Convolution · See more »
Del
Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇.
New!!: Partial differential equation and Del · See more »
Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
New!!: Partial differential equation and Derivative · See more »
Diagonal matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.
New!!: Partial differential equation and Diagonal matrix · See more »
Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
New!!: Partial differential equation and Differential equation · See more »
Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
New!!: Partial differential equation and Differential geometry · See more »
Dirichlet boundary condition
In mathematics, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859).
New!!: Partial differential equation and Dirichlet boundary condition · See more »
Discontinuous Galerkin method
In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations.
New!!: Partial differential equation and Discontinuous Galerkin method · See more »
Discriminant
In algebra, the discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them.
New!!: Partial differential equation and Discriminant · See more »
Divergence theorem
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a result that relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface.
New!!: Partial differential equation and Divergence theorem · See more »
Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
New!!: Partial differential equation and Dynamical system · See more »
Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
New!!: Partial differential equation and Eigenvalues and eigenvectors · See more »
Elasticity (physics)
In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.
New!!: Partial differential equation and Elasticity (physics) · See more »
Electrostatics
Electrostatics is a branch of physics that studies electric charges at rest.
New!!: Partial differential equation and Electrostatics · See more »
Elliptic partial differential equation
Second order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic.
New!!: Partial differential equation and Elliptic partial differential equation · See more »
Euler–Tricomi equation
In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow.
New!!: Partial differential equation and Euler–Tricomi equation · See more »
Extended finite element method
The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM).
New!!: Partial differential equation and Extended finite element method · See more »
Finite difference
A finite difference is a mathematical expression of the form.
New!!: Partial differential equation and Finite difference · See more »
Finite difference method
In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations, in which finite differences approximate the derivatives.
New!!: Partial differential equation and Finite difference method · See more »
Finite element method
The finite element method (FEM), is a numerical method for solving problems of engineering and mathematical physics.
New!!: Partial differential equation and Finite element method · See more »
Finite volume method
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations.
New!!: Partial differential equation and Finite volume method · See more »
Fluid
In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress.
New!!: Partial differential equation and Fluid · See more »
Fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.
New!!: Partial differential equation and Fluid dynamics · See more »
Fourier analysis
In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.
New!!: Partial differential equation and Fourier analysis · See more »
Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
New!!: Partial differential equation and Fourier series · See more »
Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
New!!: Partial differential equation and Fourier transform · See more »
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
New!!: Partial differential equation and Function (mathematics) · See more »
Fundamental solution
In mathematics, a fundamental solution for a linear partial differential operator is a formulation in the language of distribution theory of the older idea of a Green's function (although unlike Green's functions, fundamental solutions do not address boundary conditions).
New!!: Partial differential equation and Fundamental solution · See more »
Green's function
In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential equation defined on a domain, with specified initial conditions or boundary conditions.
New!!: Partial differential equation and Green's function · See more »
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
New!!: Partial differential equation and Group theory · See more »
Heat
In thermodynamics, heat is energy transferred from one system to another as a result of thermal interactions.
New!!: Partial differential equation and Heat · See more »
Heat equation
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.
New!!: Partial differential equation and Heat equation · See more »
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems.
New!!: Partial differential equation and Heat transfer · See more »
Helmholtz equation
In mathematics & physics, the Helmholtz equation, named for Hermann von Helmholtz, is the partial differential equation where ∇2 is the Laplacian, k is the wavenumber, and A is the amplitude.
New!!: Partial differential equation and Helmholtz equation · See more »
Homogeneous polynomial
In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.
New!!: Partial differential equation and Homogeneous polynomial · See more »
Homotopy analysis method
The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear ordinary/partial differential equations.
New!!: Partial differential equation and Homotopy analysis method · See more »
Homotopy principle
In mathematics, the homotopy principle (or h-principle) is a very general way to solve partial differential equations (PDEs), and more generally partial differential relations (PDRs).
New!!: Partial differential equation and Homotopy principle · See more »
Hp-FEM
hp-FEM is a general version of the finite element method (FEM), a numerical method for solving partial differential equations based on piecewise-polynomial approximations that employs elements of variable size (h) and polynomial degree (p).
New!!: Partial differential equation and Hp-FEM · See more »
Hyperbolic partial differential equation
In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives.
New!!: Partial differential equation and Hyperbolic partial differential equation · See more »
Impulse response
In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse.
New!!: Partial differential equation and Impulse response · See more »
Infinitesimal transformation
In mathematics, an infinitesimal transformation is a limiting form of small transformation.
New!!: Partial differential equation and Infinitesimal transformation · See more »
Integral transform
In mathematics, an integral transform maps an equation from its original domain into another domain where it might be manipulated and solved much more easily than in the original domain.
New!!: Partial differential equation and Integral transform · See more »
Jet bundle
In differential topology, the jet bundle is a certain construction that makes a new smooth fiber bundle out of a given smooth fiber bundle.
New!!: Partial differential equation and Jet bundle · See more »
Klein–Gordon equation
The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation.
New!!: Partial differential equation and Klein–Gordon equation · See more »
Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
New!!: Partial differential equation and Laplace operator · See more »
Laplace transform applied to differential equations
The Laplace transform is a powerful integral transform used to switch a function from the time domain to the s-domain.
New!!: Partial differential equation and Laplace transform applied to differential equations · See more »
Laplace's equation
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
New!!: Partial differential equation and Laplace's equation · See more »
Lax pair
In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential equation, called the Lax equation.
New!!: Partial differential equation and Lax pair · See more »
Lewy's example
In the mathematical study of partial differential equations, Lewy's example is a celebrated example, due to Hans Lewy, of a linear partial differential equation with no solutions.
New!!: Partial differential equation and Lewy's example · See more »
Lie algebra
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
New!!: Partial differential equation and Lie algebra · See more »
Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
New!!: Partial differential equation and Lie group · See more »
Lie theory
In mathematics, the researcher Sophus Lie initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory.
New!!: Partial differential equation and Lie theory · See more »
Linear function
In mathematics, the term linear function refers to two distinct but related notions.
New!!: Partial differential equation and Linear function · See more »
List of dynamical systems and differential equations topics
This is a list of dynamical system and differential equation topics, by Wikipedia page.
New!!: Partial differential equation and List of dynamical systems and differential equations topics · See more »
Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
New!!: Partial differential equation and Logical consequence · See more »
Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
New!!: Partial differential equation and Mathematical analysis · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Partial differential equation and Mathematics · See more »
Matrix differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders.
New!!: Partial differential equation and Matrix differential equation · See more »
Meshfree methods
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbours.
New!!: Partial differential equation and Meshfree methods · See more »
Method of characteristics
In mathematics, the method of characteristics is a technique for solving partial differential equations.
New!!: Partial differential equation and Method of characteristics · See more »
Method of quantum characteristics
Quantum characteristics are phase-space trajectories that arise in the phase space formulation of quantum mechanics through the Wigner transform of Heisenberg operators of canonical coordinates and momenta.
New!!: Partial differential equation and Method of quantum characteristics · See more »
Multidimensional system
In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one dependent variable exists (like time), but there are several independent variables.
New!!: Partial differential equation and Multidimensional system · See more »
Multigrid method
Multigrid (MG) methods in numerical analysis are algorithms for solving differential equations using a hierarchy of discretizations.
New!!: Partial differential equation and Multigrid method · See more »
Multivariable calculus
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one.
New!!: Partial differential equation and Multivariable calculus · See more »
Neumann boundary condition
In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann.
New!!: Partial differential equation and Neumann boundary condition · See more »
Nonlinear Schrödinger equation
In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation.
New!!: Partial differential equation and Nonlinear Schrödinger equation · See more »
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
New!!: Partial differential equation and Numerical analysis · See more »
Numerical partial differential equations
Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
New!!: Partial differential equation and Numerical partial differential equations · See more »
Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
New!!: Partial differential equation and Ordinary differential equation · See more »
Overdetermined system
In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.
New!!: Partial differential equation and Overdetermined system · See more »
Parabolic partial differential equation
A parabolic partial differential equation is a type of partial differential equation (PDE).
New!!: Partial differential equation and Parabolic partial differential equation · See more »
Partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
New!!: Partial differential equation and Partial derivative · See more »
Partial differential algebraic equation
In mathematics a partial differential algebraic equation (PDAE) set is an incomplete system of partial differential equations that is closed with a set of algebraic equations.
New!!: Partial differential equation and Partial differential algebraic equation · See more »
Perturbation theory
Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.
New!!: Partial differential equation and Perturbation theory · See more »
Phase space formulation
The phase space formulation of quantum mechanics places the position and momentum variables on equal footing, in phase space.
New!!: Partial differential equation and Phase space formulation · See more »
Picard–Lindelöf theorem
In mathematics, in the study of differential equations, the Picard–Lindelöf theorem, Picard's existence theorem or Cauchy–Lipschitz theorem is an important theorem on existence and uniqueness of solutions to first-order equations with given initial conditions.
New!!: Partial differential equation and Picard–Lindelöf theorem · See more »
Poisson's equation
In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics.
New!!: Partial differential equation and Poisson's equation · See more »
Pressure
Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
New!!: Partial differential equation and Pressure · See more »
Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
New!!: Partial differential equation and Probability distribution · See more »
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
New!!: Partial differential equation and Quadratic form · See more »
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
New!!: Partial differential equation and Quantum mechanics · See more »
Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
New!!: Partial differential equation and Recurrence relation · See more »
Rigid body
In physics, a rigid body is a solid body in which deformation is zero or so small it can be neglected.
New!!: Partial differential equation and Rigid body · See more »
Robin boundary condition
In mathematics, the Robin boundary condition (properly), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897).
New!!: Partial differential equation and Robin boundary condition · See more »
Separable partial differential equation
A separable partial differential equation (PDE) is one that can be broken into a set of separate equations of lower dimensionality (fewer independent variables) by a method of separation of variables.
New!!: Partial differential equation and Separable partial differential equation · See more »
Signal processing
Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.
New!!: Partial differential equation and Signal processing · See more »
Sophus Lie
Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician.
New!!: Partial differential equation and Sophus Lie · See more »
Sound
In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.
New!!: Partial differential equation and Sound · See more »
Spectral element method
In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high degree piecewise polynomials as basis functions.
New!!: Partial differential equation and Spectral element method · See more »
Split-step method
In numerical analysis, the split-step (Fourier) method is a pseudo-spectral numerical method used to solve nonlinear partial differential equations like the nonlinear Schrödinger equation.
New!!: Partial differential equation and Split-step method · See more »
Stochastic partial differential equation
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations.
New!!: Partial differential equation and Stochastic partial differential equation · See more »
Stochastic processes and boundary value problems
In mathematics, some boundary value problems can be solved using the methods of stochastic analysis.
New!!: Partial differential equation and Stochastic processes and boundary value problems · See more »
Supercomputer
A supercomputer is a computer with a high level of performance compared to a general-purpose computer.
New!!: Partial differential equation and Supercomputer · See more »
Superposition principle
In physics and systems theory, the superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually.
New!!: Partial differential equation and Superposition principle · See more »
Temperature
Temperature is a physical quantity expressing hot and cold.
New!!: Partial differential equation and Temperature · See more »
Underdetermined system
In mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns (in contrast to an overdetermined system, where there are more equations than unknowns).
New!!: Partial differential equation and Underdetermined system · See more »
Uniform convergence
In the mathematical field of analysis, uniform convergence is a type of convergence of functions stronger than pointwise convergence.
New!!: Partial differential equation and Uniform convergence · See more »
Uniqueness quantification
In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists.
New!!: Partial differential equation and Uniqueness quantification · See more »
Wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves.
New!!: Partial differential equation and Wave equation · See more »
Weak solution
In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense.
New!!: Partial differential equation and Weak solution · See more »
Well-posed problem
The mathematical term well-posed problem stems from a definition given by Jacques Hadamard.
New!!: Partial differential equation and Well-posed problem · See more »
Wigner quasiprobability distribution
The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution.
New!!: Partial differential equation and Wigner quasiprobability distribution · See more »
Redirects here:
Analytical solutions of partial differential equations, Classification of partial differential equations, Linear PDEs, Linear partial differential equation, Numerical solutions of partial differential equations, P.d.e., PDEs, Partial Differential Equation, Partial Differential Equations, Partial differential equation theory, Partial differential equations.
References
[1] https://en.wikipedia.org/wiki/Partial_differential_equation