Taylor-Galerkin and Taylor-collocation methods for the numerical solutions of Burgers' equation using B-splines


Dag İ. , Canivar A., Sahin A.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.16, no.7, pp.2696-2708, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 7
  • Publication Date: 2011
  • Doi Number: 10.1016/j.cnsns.2010.10.009
  • Title of Journal : COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Page Numbers: pp.2696-2708

Abstract

In this paper, for the numerical solution of Burgers' equation, we give two B-spline finite element algorithms which involve a collocation method with cubic B-splines and a Galerkin method with quadratic B-splines. In time discretization of the equation, Taylor series expansion is used. In order to verify the stabilities of the purposed methods, von-Neumann stability analysis is employed. To see the accuracy of the methods, L-2 and L-infinity error norms are calculated and obtained results are compared with some earlier studies. (C) 2010 Elsevier B.V. All rights reserved.