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 | References | Similar Articles | Additional Information

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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*Appl. Math. Comput.*(In press.) I. M. Longman, "Numerical Laplace transform inversion of a function arising in viscoelasticity,"

*J. Comput. Phys.*, v. 10, 1972, pp. 224-231. I. M. Longman, "On the generation of rational approximations for Laplace transform inversion with an application to viscoelasticity,"

*SIAM J. Appl. Math.*, v. 24, 1973, pp. 429-440. I. M. Longman, private communication, 1979.

*Numer. Math.*(In press.)

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Article copyright:
© Copyright 1982
American Mathematical Society