Evaluating a double integral using Euler's method and Richardson extrapolation

05/12/2023

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by   J. S. C. Prentice, et al.

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We transform a double integral into a second-order initial value problem, which we solve using Euler's method and Richardson extrapolation. For an example we consider, we achieve accuracy close to machine precision (1e-15). We also use the algorithm to determine the error curve for a Simpson cubature rule.