Difference between revisions of "Numerical integration"
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| − | 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 the numerical solution of differential equations. | + | 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 the [[Numerical methods for ordinary differential equations|numerical solution of differential equations]]. |
This article focuses on calculation of definite integrals. | This article focuses on calculation of definite integrals. | ||
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== Description == | == Description == | ||
| − | The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals. | + | The term numerical [[Quadrature (mathematics)|quadrature]] (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals. |
Some authors refer to numerical integration over more than one dimension as cubature; others take quadrature to include higher-dimensional integration. | Some authors refer to numerical integration over more than one dimension as cubature; others take quadrature to include higher-dimensional integration. | ||
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* [[Clenshaw–Curtis quadrature]] | * [[Clenshaw–Curtis quadrature]] | ||
* [[Gauss-Kronrod quadrature]] | * [[Gauss-Kronrod quadrature]] | ||
| + | * [[Numerical methods for ordinary differential equations]] | ||
* [[Numerical ordinary differential equations]] | * [[Numerical ordinary differential equations]] | ||
| + | * [[Quadrature (mathematics)]] | ||
* [[Riemann Sum or Riemann Integral]] | * [[Riemann Sum or Riemann Integral]] | ||
* [[Trapezoidal Rule]] | * [[Trapezoidal Rule]] | ||
Latest revision as of 11:45, 21 September 2016
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 the numerical solution of differential equations.
This article focuses on calculation of definite integrals.
Description
The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Some authors refer to numerical integration over more than one dimension as cubature; others take quadrature to include higher-dimensional integration.
See also
- Clenshaw–Curtis quadrature
- Gauss-Kronrod quadrature
- Numerical methods for ordinary differential equations
- Numerical ordinary differential equations
- Quadrature (mathematics)
- Riemann Sum or Riemann Integral
- Trapezoidal Rule
- Truncation error (numerical integration)
External links
- Numerical integration @ Wikipedia
