Description
With this free course of 69 video lessons, you will learn about the most important concepts of Numerical Integration
In numerical analysis, numerical integration constitutes a wide range of algorithms for calculating the numerical value of a definite integral and, by extension, the term is sometimes used to describe numerical algorithms for solving differential equations. The term numerical quadrature (often abbreviated to quadrature) is more or less synonymous with numerical integration, especially if it is applied to one-dimensional integrals even though for the case of two or more dimensions (multiple integral) it is also used.
The basic problem considered by numerical integration is to compute an approximate solution to the definite integral:
This problem can also be stated as an initial value problem for an ordinary differential equation, as follows:
Finding y(b) is equivalent to calculating the integral. Methods developed for ordinary differential equations, such as the Runge-Kutta method, can be applied to the reformulated problem. This article discusses methods developed specifically for the problem formulated as a definite integral.
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