Numerical Solution and error analysis of Fredholm Integro-differential equation by using Legendre and Block Pulse functions

DOI: 10.5176/2251-1911_CMCGS15.14

Authors: Bijil Prakash, and Amit Setia

Abstract:  This paper introduces an approach for obtaining the numerical solution of the Fredholm integro-differential equations by using hybrid Legendre polynomials and Block-Pulse functions. The operational matrices of above hybrid functions are used for representing matrix form of the integro-differential equations. The main characteristic of this approach is that it reduces Fredholm integro-differential equations to a system of algebraic equations, which greatly simplifies the problem. Numerical examples illustrate the validity, applicability and the convergence behavior of the proposed method.

Keywords: Integro-differential equation, Operational matrix, Hybrid functions, Legendre polynomials, Block-Pulse functions