Numerical solution of system of Fredholm-Volterra integro-differential equations using Legendre polynomials

In this paper, two collocation methods based on the shifted Legendre polynomials are proposed for solving system of nonlinear Fredholm-Volterra integro-differential equations. The equation considered in paper involves derivative unknown functions integral term, which makes its numerical solution more complicated. We first introduce a single-step method interval [0, 1]. Next, multi-step version is derived arbitrary T] that domain decomposition strategy and specially suited large calculations. scheme converts problem to algebraic equations whereas later solves step by subintervals produces sequence systems Some error estimates investigated. Numerical examples given comparisons with other available literature done demonstrate high accuracy efficiency methods.