Solution of nonlinear ordinary differential equations with quadratic and cubic terms by Morgan-Voyce matrix-collocation method

Abstract

Nonlinear differential equations have many applications in different science and engineering disciplines.However, a nonlinear differential equation cannot be solved analytically and so must be solved numerically. Thus, weaim to develop a novel numerical algorithm based on Morgan-Voyce polynomials with collocation points and operationalmatrix method to solve nonlinear differential equations. In the our proposed method, the nonlinear differential equationsincluding quadratic and cubic terms having the initial conditions are converted to a matrix equation. In order to obtainthe matrix equations and solutions for the selected problems, code was developed in MATLAB. The solution of thismethod for the convergence and efficiency was compared with the equations such as Van der Pol differential equationcalculated by different methods.