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

Authors

MEHMET TARAKÇI
MUSTAFA ÖZEL
MEHMET SEZER

DOI

10.3906/mat-1908-102

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, we aim to develop a novel numerical algorithm based on Morgan-Voyce polynomials with collocation points and operational matrix method to solve nonlinear differential equations. In the our proposed method, the nonlinear differential equations including quadratic and cubic terms having the initial conditions are converted to a matrix equation. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB. The solution of this method for the convergence and efficiency was compared with the equations such as Van der Pol differential equation calculated by different methods.

Keywords

Nonlinear ordinary differential equations, Morgan-Voyce polynomials, matrix-collocation method, residual error analysis

First Page

906

Last Page

918

Recommended Citation

TARAKÇI, MEHMET; ÖZEL, MUSTAFA; and SEZER, MEHMET (2020) "Solution of nonlinear ordinary differential equations with quadratic and cubic terms by Morgan-Voyce matrix-collocation method," Turkish Journal of Mathematics: Vol. 44: No. 3, Article 20. https://doi.org/10.3906/mat-1908-102
Available at: https://journals.tubitak.gov.tr/math/vol44/iss3/20