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 the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals. Numerical integration over more than one dimension is sometimes described as cubature, although the meaning of quadrature is understood for higher dimensional integration as well.

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

If f(x) is a smooth well-behaved function, integrated over a small number of dimensions and the limits of integration are bounded, there are many methods of approximating the integral with arbitrary precision.

Read more about Numerical Integration:  Reasons For Numerical Integration, Methods For One-dimensional Integrals, Multidimensional Integrals, Connection With Differential Equations

Famous quotes containing the words numerical and/or integration:

    There is a genius of a nation, which is not to be found in the numerical citizens, but which characterizes the society.
    Ralph Waldo Emerson (1803–1882)

    The more specific idea of evolution now reached is—a change from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity, accompanying the dissipation of motion and integration of matter.
    Herbert Spencer (1820–1903)