Higher Order Accurate Numerical Solution of Advection Diffusion Equation

Abstract

In this study, the advection diffusion equation (ADE) will be solved numerically using the quintic B-spline Galerkin finite-element method, based on second and fourth order single step methods for time integration. Two test problems are studied and accuracy of the numerical results are measured by the computing the order of convergence and error norm $L_{\infty }$ for the proposed methods. The numerical results of this study demonstrate that the proposed two algorithms especially the fourth order single step method are a remarkably successful numerical technique for solving the advection diffusion equation.