An efficient and fast parallel method for Volterra integral equations of Abel type

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:189

Article; Proceedings Paper

Capobianco, G ; Conte, D

关键词: Abel equations;    parallel methods;    waveform relaxation methods;    Chebyshev polynomial;    talbot contours;   

DOI  :  10.1016/j.cam.2005.03.056

来源: Elsevier

【 摘 要 】

In this paper we present an efficient and fast parallel waveform relaxation method for Volterra integral equations of Abel type, obtained by reformulating a nonstationary waveform relaxation method for systems of equations with linear coefficient constant kernel. To this aim we consider the Laplace transform of the equation and here we apply the recurrence relation given by the Chebyshev polynomial acceleration for algebraic linear systems. Back in the time domain, we obtain a three term recursion which requires, at each iteration, the evaluation of convolution integrals, where only the Laplace transform of the kernel is known. For this calculation we can use a fast convolution algorithm. Numerical experiments have been done also on problems where it is not possible to use the original nonstationary method, obtaining good results in terms of improvement of the rate of convergence with respect the stationary method. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free