Numerical Scheme Based on Operational Matrices for Integro-Differential Equations - Singh, C.; K. Singh, A.; K. Sahoo, J. (International Journal of Engineering and Technology, 2018)
An effective numerical tool based on wavelets and orthogonal polynomials are presented for the solution of a class of system of singular Voltera integro-differential equations (SSVIDEs). We also presented the convergence analysis for the derivative of the approximation in terms of Legendre wavelets. In this paper, we propose a numerical wavelet and polynomial methods for solving SSVIDEs of second kind. The method is based on the operational and almost operational matrix of integration based on wavelet and orthogonal polynomials. We use the concept of operation matrix of integration to convert the main problem into linear system of algebraic equations. Some numerical examples along with error evaluation are given to illustrate the accuracy and efficiency of the proposed method. The advantage of the proposed technique is computationally most simple, low cost of setting the algebraic equations without using artificial smoothing factors.Â Â