On the Levin iterative method for oscillatory integrals

Authors:
Shuhuang Xiang;Haiyong Wang
Affiliations:
Department of Applied Mathematics and Software, Central South University, Changsha, Hunan 410083, China;Department of Applied Mathematics and Software, Central South University, Changsha, Hunan 410083, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

This paper considers and gives error analysis for Levin iteration method to approximate Bessel-trigonometric transformation I[f]=@!"a^bf(x)cos(r"1x)J"@m(rx)dx. For generalized Fourier transformation I[f]=@!"a^bf(x)e^i^@w^g^(^x^)dx under the condition that g^'(x)0 for all x@?[a,b], Levin iteration method with the initial U^[^0^](x)=0 is identical to the asymptotic method.