A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS

Authors : Melis ZORSAHİN GORGULU, İdris DAG, Sumeyye DOGAN, Dursun IRK

Pages : 347-355

Doi:10.18038/aubtda.336116

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Publication Date : 2018-03-31

Article Type : Research Paper

Abstract :In this paper, numerical solution of the advection-diffusion equation is obtained by using extended cubic B-spline functions. For space discretization, the extended cubic B-spline Galerkin method is used to integrate the advection-diffusion equation and for time discretization, the Crank-Nicolson method is employed to obtain the fully integrated advection-diffusion equation. The maximum error norm has been used to show the accuracy of the method. Robustness of the suggested method is shown by studying some classical test problems and comparing the results with some earlier ones.
Keywords : Extended cubic B spline, Galerkin finite element method, advection diffusion equation