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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2015 Volume 55, Number 9, Page 1511 (Mi zvmmf10264)

This article is cited in 20 papers

Sparse representation of system of Fredholm integro-differential equations by using Alpert multiwavelets

Behzad Nemati Saraya, Mehrad Lakestania, Mohsen Razzaghib

a Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
b Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA

Abstract: A numerical technique is presented for the solution of system of Fredholm integro-differential equations. The method consists of expanding the required approximate solution as the elements of Alpert multiwavelet functions (see Alpert B. et al. J. Comput. Phys. 2002, vol. 182, pp. 149–190). Using the operational matrix of integration and wavelet transform matrix, we reduce the problem to a set of algebraic equations. This system is large. We use thresholding to obtain a new sparse system; consequently, GMRES method is used to solve this new system. Numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces accurate results.

Key words: Alpert multiwavelets, Fredholm integro-differential equations, thresholding, sparse matrix, GMRES method.

UDC: 519.642.3

Received: 10.09.2013

DOI: 10.7868/S0044466915090033


 English version:
Computational Mathematics and Mathematical Physics, 2015, 55:9, 1468–1483

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