Solutions of Linear and Nonlinear Volterra Integral Equations Using Hermite and Chebyshev Polynomials

  • Md. Shafiqul Islam Dhaka University
  • Md. Azizur Rahman Bangladesh University of Business & Technology
Keywords: Linear and nonlinear Volterra integral equations, Galerkin method, Hermite and Chebyshev polynomials

Abstract

The purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on Galerkin weighted residual approximation. In this method Hermite and Chebyshev piecewise, continuous and differentiable polynomials are exploited as basis functions. A rigorous effective matrix formulation is proposed to solve the linear and nonlinear Volterra integral equations of the first and second kind with regular and singular kernels. The algorithm is simple and can be coded easily. The efficiency of the proposed method is tested on several numerical examples to get the desired and reliable good accuracy.

Author Biographies

Md. Shafiqul Islam, Dhaka University
Professor, Department of Mathematics
Md. Azizur Rahman, Bangladesh University of Business & Technology
Lecturer, Department of Mathematics
Published
2013-11-27
How to Cite
Islam, M. S., & Rahman, M. A. (2013). Solutions of Linear and Nonlinear Volterra Integral Equations Using Hermite and Chebyshev Polynomials. INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY, 11(8), 2910-2920. https://doi.org/10.24297/ijct.v11i8.3010
Section
Articles