Numerical integration

In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe numerical algorithms for solving differential equations.

Related Topics:
Numerical analysis - Integral - Differential equations

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The term quadrature is more or less a synonym for numerical integration,

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especially as applied to one-dimensional integrals. Two-dimensional integration is sometimes described as cubature, although this term is much less frequently

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used and the meaning of quadrature is understood for higher dimensional integration as well.

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The basic problem considered by numerical integration is to compute an approximate solution to a definite integral:

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:int_a^b f(x), dx

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This problem can also be stated as an initial value problem for an ordinary differential equation, as follows.

Related Topics:
Initial value problem - Ordinary differential equation

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: y'(x) = f(x), quad y(a) = 0

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Finding y(b) is equivalent to computing the integral.

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Methods developed for ordinary differential equations,

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such as the Runge-Kutta method, can be applied to the restated problem.

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In the remainder of this article,

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we shall discuss methods developed specifically for the problem stated as a definite integral.

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