numerical solution of system of nonlinear integro-differential equations using hybrid of legendre polynomials and block-pulse functions

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.