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

TARAKÇI M., ÖZEL M., Sezer M.

Turkish Journal of Mathematics, vol.44, no.3, pp.906-918, 2020 (SCI-Expanded, Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1908-102
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.906-918
  • Keywords: Matrix-collocation method, Morgan-Voyce polynomials, Nonlinear ordinary differential equations, Residual error analysis
  • Manisa Celal Bayar University Affiliated: Yes

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.