Exponential B-Spline Solution of Convection-Diffusion Equations

Reza Mohammadi

Department of Mathematics, University of Neyshabur, Neyshabur, Iran.

DOI: 10.4236/am.2013.46129                

Abstract

We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet’s type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration and exponential B-spline functions for space integration. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. Numerical experiments have been conducted to demonstrate the accuracy of the current algorithm with relatively minimal computational effort. The results showed that use of the present approach in the simulation is very applicable for the solution of convection-diffusion equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithm is seen to be very good alternatives to existing approaches for such physical applications.

Keywords

Exponential B-Spline; Convection-Diffusion Equation; Collocation; Crank-Nicolson Formulation;

Conflicts of Interest

The authors declare no conflicts of interest.

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