Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters

A high-accuracy numerical method based on a sixth-order combined compact difference scheme and the method of lines approach is proposed for the advection-diffusion transport equation with variable parameters. In this approach, the partial differential equation representing the advection-diffusion equation is converted into many ordinary differential equations. These time-dependent ordinary differential equations are then solved using an explicit fourth order Runge-Kutta method. Three test problems are studied to demonstrate the accuracy of the present methods. Numerical solutions obtained by the proposed method are compared with the analytical solutions and the available numerical solutions given in the literature. In addition to requiring less CPU time, the proposed method produces more accurate and more stable results than the numerical methods given in the literature.