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

Calder Prentice, Justin Steven

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 (~10-13). We find that the algorithm is capable of determining the error curve for an arbitrary cubature formula, and we use this feature to determine the error curve for a Simpson cubature rule. We also provide a generalization of the method to the case of nonlinear limits in the outer integral.

DOUBLE integrals; INITIAL value problems; EULER method; GENERALIZATION; ACCURACY

Lietuvos Matematikos Rinkinys, 2024, Vol 65, Issue Series A, p39

0132-2818

Academic Journal

10.15388/lmd.2024.38091