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33 relations: Applied mathematics, Basis function, Burgers' equation, Calculus, Collocation method, Computational science, Convolution, Differential equation, Eigenvalues and eigenvectors, Elliptic boundary value problem, Fast Fourier transform, Finite element method, Fourier series, Galerkin method, Gaussian grid, Gibbs phenomenon, Inner product space, Integration by parts, Kronecker delta, M. Yousuff Hussaini, Numerical methods for ordinary differential equations, Ordinary differential equation, Orthogonality, Partial differential equation, Poisson's equation, Pseudo-spectral method, Runge–Kutta methods, Shock capturing method, Sine wave, Smoothness, Spectral element method, Steven Orszag, Viscosity.
Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.
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Basis function
In mathematics, a basis function is an element of a particular basis for a function space.
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Burgers' equation
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, traffic flow.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Collocation method
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.
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Computational science
Computational science (also scientific computing or scientific computation (SC)) is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems.
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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.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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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.
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Elliptic boundary value problem
In mathematics, an elliptic boundary value problem is a special kind of boundary value problem which can be thought of as the stable state of an evolution problem.
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Fast Fourier transform
A fast Fourier transform (FFT) is an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.
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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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Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
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Galerkin method
In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem (such as a differential equation) to a discrete problem.
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Gaussian grid
A Gaussian grid is used in the earth sciences as a gridded horizontal coordinate system for scientific modeling on a sphere (i.e., the approximate shape of the Earth).
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Gibbs phenomenon
In mathematics, the Gibbs phenomenon, discovered by Available on-line at: and rediscovered by, is the peculiar manner in which the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative.
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Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
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M. Yousuff Hussaini
Mohammed Yousuff Hussaini is an Indian born American applied mathematician.
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Numerical methods for ordinary differential equations
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
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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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Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
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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'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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Pseudo-spectral method
Pseudo-spectral methods, also known as discrete variable representation (DVR) methods, are a class of numerical methods used in applied mathematics and scientific computing for the solution of partial differential equations.
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Runge–Kutta methods
In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations.
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Shock capturing method
In computational fluid dynamics, shock-capturing methods are a class of techniques for computing inviscid flows with shock waves.
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Sine wave
A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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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.
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Steven Orszag
Steven Alan Orszag (February 27, 1943 – May 1, 2011) was an American mathematician.
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Viscosity
The viscosity of a fluid is the measure of its resistance to gradual deformation by shear stress or tensile stress.
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References
[1] https://en.wikipedia.org/wiki/Spectral_method
