Quartic and quintic B-spline methods for advection-diffusion equation

Differential quadrature methods based on B-spline functions of degree four and five have been introduced to solve advection-diffusion equation numerically. Two initial-boundary value problems modeling the transportation of a concentration and distribution of an initial pulse are simulated using both methods. The errors of the numerical results obtained by both methods have been computed. Stability analysis for both methods is also studied by the use of matrix stability.