Multi-Wavelets Galerkin Method for Solving the System of Volterra Integral Equations

Hoang Viet Long, Haifa Bin Jebreen and Stefania Tomasiello
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Hoang Viet Long: Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam
Haifa Bin Jebreen: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Stefania Tomasiello: Institute of Computer Science, University of Tartu, 50090 Tartu, Estonia

Mathematics, 2020, vol. 8, issue 8, 1-14

Abstract: In this work, an efficient algorithm is proposed for solving the system of Volterra integral equations based on wavelet Galerkin method. This problem is reduced to a set of algebraic equations using the operational matrix of integration and wavelet transform matrix. For linear type, the computational effort decreases by thresholding. The convergence analysis of the proposed scheme has been investigated and it is shown that its convergence is of order O ( 2 − J r ) , where J is the refinement level and r is the multiplicity of multi-wavelets. Several numerical tests are provided to illustrate the ability and efficiency of the method.

Keywords: Volterra integral equations; operational matrix of integration; multi-wavelets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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