Numerical Solution of Advection-Diffusion Equation by a Modified Cubic B-Spline Collocation Method

Abstract

In this work, advection-diffusion equation (ADE) has been studied by using a modified cubic B-spline numerical method. This method produces good results with high accuracy. We have discretized the advection-diffusion equation using the finite difference method. To demonstrate the fourth-order convergence of the proposed method, error analysis is performed. A stability analysis is done by Von-Neumann method and the method is shown to be unconditionally stable. Seven different advection-diffusion equations with Periodic, Neumann, and Dirichlet boundary conditions have been solved to test the effectiveness of the proposed method. The results from these examples highlight the benefits of the method, and comparisons with other methods reveal that the proposed method performs better.