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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
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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Article copyright: © Copyright 1982 American Mathematical Society

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