Numerical Solution of System of Nonlinear Integro-Differential Equations Using Hybrid of Legendre Polynomials and Block-Pulse Functions

Document Type: Original Scientific Paper


1 Department of applied mathematics, faculty of mathematical sciences, University of Kashan, Kashan, Iran.

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran



In this paper, numerical techniques are presented for solving system of nonlinear integro-differential equations. The method is implemented by applying hybrid of Legendre polynomials and block-pulse functions. The operational matrix of integration and the integration of the cross product of two hybrid function vectors are derived in order to transform the system of nonlinear integro-differential equations into a system of algebraic equations. Finally, the accuracy of the method is illustrated through some numerical examples and the corresponding results are presented.