A numerical Approach for solving classes of Linear and Nonlinear Volterra Integral Equations by Chebyshev polynomial

Abstract

In this paper we propose a numerical method for solving classes of of linear and nonlinear Volterraintegral equations having regular as well as weakly singular kernels. The method is based upon replacingthe unknown function by a truncated shifted Chebyshev series. This yeilds either a linear system ofalgebraic equations that can be solved using matrix algebra or a nonlinear system that can be solved byNewton’s iterative method. This method is effective and so easy to apply with low cost of computingoperations. The accuracy and efficiency of the method can be shown through the illustrated numericalexamples.keywords: Volterra integral equations, Newton’s method, Simpson’s method, Chebyshev polynomials,Shifted Chebyshev polynomials.Mathematics Subject Classification: 45B05 , 45Bxx , 65R10