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6: Integration

Last updated

May 31, 2022
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- 5.4: Multidimensional Interpolation
- 6.1: Elementary Formulas

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We want to construct numerical algorithms that can perform definite integrals of the form

$I=\int_{a}^{b} f(x) d x \nonumber$

Calculating these definite integrals numerically is called numerical integration, numerical quadrature, or more simply quadrature.

6.1: Elementary Formulas
6.2: Composite Rules
6.3: Local Versus Global Error
6.4: Adaptive Integration
The useful MATLAB function quad.m performs numerical integration using adaptive Simpson quadrature. The idea is to let the computation itself decide on the grid size required to achieve a certain level of accuracy. Moreover, the grid size need not be the same over the entire region of integration.

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