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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- © Copyright 1982 American Mathematical Society
- 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