The numerical evaluation of very oscillatory infinite integrals by extrapolation

Author:
Avram Sidi

Journal:
Math. Comp. **38** (1982), 517-529

MSC:
Primary 65D30; Secondary 41A55, 65B99

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645667-5

MathSciNet review:
645667

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Abstract: Recently the author has given two modifications of a nonlinear extrapolation method due to Levin and Sidi, which enable one to accurately and economically compute certain infinite integrals whose integrands have a simple oscillatory behavior at infinity. In this work these modifications are extended to cover the case of very oscillatory infinite integrals whose integrands have a complicated and increasingly rapid oscillatory behavior at infinity. The new method is applied to a number of complicated integrals, among them the solution to a problem in viscoelasticity. Some convergence results for this method are presented.

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0645667-5

Article copyright:
© Copyright 1982
American Mathematical Society