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On the calculation of highly oscillatory integrals with an algebraic singularity

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
217
Issue
8
Identifiers
DOI: 10.1016/j.amc.2010.09.050
Keywords
  • Oscillatory Integrals
  • Change Of Variable
  • Steepest Descent Method
Disciplines
  • Mathematics

Abstract

Abstract In this paper we explore the evaluation of highly oscillatory integrals containing an algebraic singularity based on the change of variable t = x − r , where r is a positive real number, and the analytical continuation. Robust numerical results demonstrate the accuracy and effectiveness of the proposed approach.

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