Gaussian quadrature with change of variables

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Melanie Wroblewski 2022-11-29

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回答： Andreas Apostolatos 2022-11-29

I need help writing a matlab function that numerically integrates any continuous function f (x, y) over the parallelogram (1, 1), (3, 2), (4, 4) and (6, 5) using Gaussian quadrature with m × n points. The inputs of your function must be f , m and n.

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Answer 1

Andreas Apostolatos 2022-11-29

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Hi Melanie,

There are serveral submissions on File Exchange that you can use to compute integrals using the Gauss Quadrature rule. Please check the following post on MATLAB Answers and in particular the comprehensive answer from John D'Errico:

https://www.mathworks.com/matlabcentral/answers/426221-is-there-a-matlab-code-for-gaussion-integration

Among other, he also shows comprehensive examples on how this can be done for one-dimensional functions f(x). For two-dimensional functions f(x,y) you simply needed a nested loop. This is also very nicely shown in the following MATLAB Answers post,

https://www.mathworks.com/matlabcentral/answers/256-2d-quadrature-for-an-array-valued-function

I hope this helps.

Kind regards

Andreas