Modified Legendre Operator Matrix for Nonlinear IVP.

In this paper, we derive the operator matrix of differentiation (OMD) for the Legender polynomials in the closed interval of the form [a, b], where a, b - R. Then, we use this OMD to solve a system of nonlinear initial value problem for long time span. For that, we propose algorithm that depends on dividing the interval of the solution into a finite subintervals and apply the OMD to each subinterval. This algorithm leads to accurate solution for long time span. Genesio system in chaotic case is considered to demonstrate the efficiency of this algorithm. [ABSTRACT FROM AUTHOR]