On the Numerical Solution of Linear Advection-Diffusion Equation using Compactly Supported Radial Basis Functions

We present a meshless method based on compactly supported radial basis functions to find a stable and accurate solution for the numerical solution of linear advection-diffusion equation. The efficiency of the method in terms of computational processing time, accuracy and stability is also discussed. The results are compared with the findings from the thin plate spline radial basis function and finite difference methods. Our analysis shows that compactly supported radial basis functions method, with its simple implementation, generates excellent results and speeds up the computational processing time, independent of the shape of the domain and irrespective of the dimension of the problem.