AN APPLICATION OF CUBIC B-SPLINE FINITE ELEMENT METHOD FOR THE BURGERS' EQUATION


AKSAN E. N.

THERMAL SCIENCE, vol.22, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22
  • Publication Date: 2018
  • Doi Number: 10.2298/tsci170613286a
  • Journal Name: THERMAL SCIENCE
  • Journal Indexes: Science Citation Index Expanded, Scopus

Abstract

It is difficult to achieve exact solution of non-linear PDE, directly. Sometimes, it is possible to convert non-linear PDE into equivalent linear PDE by applying a convenient transformation. Hence, Burgers' equation replaces with heat equation by means of the Hope-Cole transformation. In this study, Burgers' equation was converted to a set of non-linear ODE by keeping non-linear structure of Burgers' equation. In this case, solutions for each of the non-linear ODE were obtained by the help of the cubic B-spline finite element method. Model problems were considered to verify the efficiency of this method. Agreement of the solutions was shown with graphics and tables.