An application of cubic B-Spline finite element method for the Burgers` equation | Zendy

E.N. Aksan | Zendy

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An application of cubic B-Spline finite element method for the Burgers` equation

Author(s) -

E.N. Aksan

Publication year - 2017

Publication title -

thermal science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.339

H-Index - 43

eISSN - 2334-7163

pISSN - 0354-9836

DOI - 10.2298/tsci170613286a

Subject(s) - burgers' equation , ode , finite element method , b spline , mathematics , transformation (genetics) , mathematical analysis , partial differential equation , physics , thermodynamics , biochemistry , chemistry , gene

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.

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