The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics

Abstract

In this study, the Legendre operational matrix method based on collocation points is introduced to solve high order ordinary differentialequations with some nonlinear terms arising in physics and mechanics. This technique transforms the nonlinear differential equationinto a matrix equation with unknown Legendre coefficients via mixed conditions. This solution of this matrix equation yields theLegendre coefficients of the solution function. Thus, the approximate solution is obtained in terms of Legendre polynomials. Some testproblems together with residual error estimation are given to show the usefulness and applicability of the method and the numericalresults are compared.