An Exponential Cubic B-spline Algorithm for Solving the Nonlinear Coupled Burgers’ Equation

Ersoy Hepson Ö., Dağ İ.

Computational Methods for Differential Equations, vol.9, no.4, pp.1109-1127, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.22034/cmde.2020.39486.1727
  • Journal Name: Computational Methods for Differential Equations
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.1109-1127
  • Keywords: Coupled Burgers' equation, Exponential cubic B-spline, Stability analysis, Collocation, DIFFERENTIAL QUADRATURE METHOD, NUMERICAL-SOLUTIONS, COLLOCATION METHOD, SIMULATION, SYSTEMS, SCHEME
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

The collocation method based on the exponential cubic B-splines (ECB-splines) together with the Crank-Nicolson formula is used to solve nonlinear coupled Burgers' equation (CBE). This method is tested by studying three different problems. The proposed scheme is compared with some existing methods. It produced accurate results with the suitable selection of the free parameter of the ECB-spline function. It produces accurate results. Stability of the fully discretized CBE is investigated by the Von Neumann analysis.