A parallel algorithm for large systems of Volterra integral equations of Abel type |
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Authors: | G Capobianco A Cardone |
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Institution: | aDipartimento S.T.A.T., Università del Molise, Contrada Fonte Lappone, I-86090 Pesche (IS), Italy;bDipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Via Cintia, I-80126 Napoli, Italy |
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Abstract: | A significative number of recent applications require numerical solution of large systems of Abel–Volterra integral equations. Here we propose a parallel algorithm to numerically solve a class of these systems, designed for a distributed-memory MIMD architecture. In order to achieve a good efficiency we employ a fully parallel and fast convergent waveform relaxation (WR) method and evaluate the lag term by using FFT techniques. To accelerate the convergence of the WR method and to best exploit the parallel architecture we develop special strategies. The performances of the resulting code, NSWR4, are illustrated on some examples. |
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Keywords: | Volterra– Abel integral equations Waveform relaxation methods Fractional linear methods Fast Fourier transform Parallel algorithm |
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