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50 relations: Alternating direction implicit method, Atiyah–Singer index theorem, Bäcklund transform, Boundary element method, Boundary value problem, Broer–Kaup equations, Calculus of variations, Cauchy–Kowalevski theorem, Computational fluid dynamics, Dirichlet boundary condition, Dirichlet problem, Elliptic partial differential equation, Finite difference, Finite element method, Finite volume method, Green's function, Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation, Harmonic analysis, Harmonic function, Heat equation, Homotopy principle, Klein–Gordon equation, Korteweg–de Vries equation, Laplace operator, Laplace's equation, List of nonlinear partial differential equations, List of things named after Leonhard Euler, Maxwell's equations, Modified KdV–Burgers equation, Multigrid method, Navier–Stokes equations, Neumann boundary condition, Nonlinear partial differential equation, Ordinary differential equation, Partial differential equation, Poisson kernel, Poisson's equation, Primitive equations, Schrödinger equation, Separation of variables, Singular perturbation, Sobolev space, Spectral method, Spherical harmonics, Stefan problem, Viscosity solution, Wave equation, Weak solution, Wiener–Hopf method.
Alternating direction implicit method
In numerical linear algebra, the Alternating Direction Implicit (ADI) method is an iterative method used to solve Sylvester matrix equations.
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Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by, states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).
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Bäcklund transform
In mathematics, Bäcklund transforms or Bäcklund transformations (named after the Swedish mathematician Albert Victor Bäcklund) relate partial differential equations and their solutions.
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Boundary element method
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form).
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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.
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Broer–Kaup equations
The Broer–Kaup equations are a set of two coupled nonlinear partial differential equations.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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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.
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Computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to solve and analyze problems that involve fluid flows.
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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).
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Dirichlet problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region.
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Elliptic partial differential equation
Second order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic.
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Finite difference
A finite difference is a mathematical expression of the form.
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Finite element method
The finite element method (FEM), is a numerical method for solving problems of engineering and mathematical physics.
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Finite volume method
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations.
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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.
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Hamilton–Jacobi equation
In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman equation.
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Hamilton–Jacobi–Bellman equation
The Hamilton–Jacobi–Bellman (HJB) equation is a partial differential equation which is central to optimal control theory.
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Harmonic analysis
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis).
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Harmonic function
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U → R where U is an open subset of Rn that satisfies Laplace's equation, i.e. everywhere on U. This is usually written as or.
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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.
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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).
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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.
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Korteweg–de Vries equation
In mathematics, the Korteweg–de Vries equation (KdV equation for short) is a mathematical model of waves on shallow water surfaces.
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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.
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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.
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List of nonlinear partial differential equations
See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations.
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List of things named after Leonhard Euler
Leonhard Euler (1707–1783)In mathematics and physics, there are a large number of topics named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations.
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Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
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Modified KdV–Burgers equation
The modified KdV–Burgers equation is a nonlinear partial differential equation.
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Multigrid method
Multigrid (MG) methods in numerical analysis are algorithms for solving differential equations using a hierarchy of discretizations.
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Navier–Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.
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Neumann boundary condition
In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann.
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Nonlinear partial differential equation
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms.
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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.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Poisson kernel
In potential theory, the Poisson kernel is an integral kernel, used for solving the two-dimensional Laplace equation, given Dirichlet boundary conditions on the unit disc.
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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.
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Primitive equations
The primitive equations are a set of nonlinear differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models.
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Schrödinger equation
In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.
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Separation of variables
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.
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Singular perturbation
In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero.
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Sobolev space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function itself and its derivatives up to a given order.
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Spectral method
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the Fast Fourier Transform.
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Spherical harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere.
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Stefan problem
In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem (also Stefan task) is a particular kind of boundary value problem for a partial differential equation (PDE), adapted to the case in which a phase boundary can move with time.
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Viscosity solution
In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael G. Crandall as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE).
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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.
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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.
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Wiener–Hopf method
The Wiener–Hopf method is a mathematical technique widely used in applied mathematics.
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References
[1] https://en.wikipedia.org/wiki/List_of_partial_differential_equation_topics
