SOR Iterative Method with Wave Variable Transformation for Solving Advection-Diffusion Equations

In this study, problem of partial differential equations (PDEs) especially one-dimensional (1D) advection-diffusion equation has been reduced to the corresponding second-order ordinary differential equation (ODE) through the transformation of wave variables. Next, we need to discretize ODE inorder to derive the second order approximation equation. Furthermore, this approximation equation is considered to develop a system of linear equations. In addition, the successive over relaxation (SOR) iterative method has been used to solve the generated system of linear equations. For the purpose of comparison, three comparative parameters were used to analyze the performance of SOR method such as the number of iteration, the computational time, and the maximum error. Based on the numerical results obtained from gauss-seidal(GS) and SOR methods, it can be pointed out that SOR method is more efficient than the GS method.