Galerkin Method for the Numerical Solution of the Advection-Diffusion Equation by Using Exponential B-splines

Subject Areas : International Journal of Mathematical Modelling & Computations

Melis  Zorsahin Gorgulu ¹ (Department of Mathematics-Computer, Faculty of Science and Art, Eskisehir Osmangazi University, Eskisehir, Turkey)
Idris  Dag ² (Department of Computer Engineering, Faculty of Engineering and Architecture, Eskisehir Osmangazi University, Eskisehir, Turkey)

Received: 2017-12-08 Accepted : 2018-11-11 Published : 2018-08-01

Keywords: Galerkin Method, Crank-Nicolson method, Exponential B-Spline, Advection-Diffusion Equation,

Abstract :

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.