Numerical solution of Volterra integral equation and its error estimates via Spectral method

Abstract

In this article, numerical solution of Volterra integral equations is considered. A new approach in the application of spectral method is proposed, wherein Chebyshev polynomial of the first kind T (x) k serves as the basis function. Essentially, the method is based on the approach of series solution where coefficients of T (x) k in the residual equations are correspondingly equated to yield system of equations. Expression for error estimates which effectively serves as upper bound for accrued errors is arrived at. To illustrate the accuracy and effectiveness of the method and its error estimates, numerical examples on some standard integral equations are given.