Numerical Solutions of Volterra Integral Equations Using Laguerre Polynomials

Authors

  • M. A. Rahman
  • M. S. Islam
  • M. M. Alam

DOI:

https://doi.org/10.3329/jsr.v4i2.9407

Keywords:

Volterra integral equation, Galerkin method, Laguerre polynomials

Abstract

We solve numerically Volterra integral equations, of first and second kind with regular and singular kernels, by the well known Galerkin weighted residual method. For this, we derive a simple and efficient matrix formulation using Laguerre polynomials as trial functions. Several numerical examples are tested. The approximate solutions of some examples coincide with the exact solutions on using a very few Laguerre polynomials. The approximate results, obtained by the present method, confirm the convergence of numerical solutions and are compared with the existing methods available in the literature.

Keywords: Volterra integral equations; Galerkin method; Laguerre polynomials.

© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi: http://dx.doi.org/10.3329/jsr.v4i2.9407    J. Sci. Res. 4 (2), 357-364 (2012)

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Author Biographies

M. A. Rahman

Department of Mathematics & Statistics
Bangladesh University of Business & Technology, Dhaka

M. S. Islam

Department of Mathematics
University of Dhaka

M. M. Alam

Mathematics Discipline
Khulna University, Khulna

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Published

2012-04-22

How to Cite

Rahman, M. A., Islam, M. S., & Alam, M. M. (2012). Numerical Solutions of Volterra Integral Equations Using Laguerre Polynomials. Journal of Scientific Research, 4(2), 357. https://doi.org/10.3329/jsr.v4i2.9407

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Section

Section A: Physical and Mathematical Sciences