Numerical Solution of One-Dimensional Advection-Diffusion Equation using Radial Basis Function Method of Lines

Abstract

The research article proposes a numerical solution for the one-dimensional advection-diffusion equation using the Radial Basis Function (RBF) method of lines. The approach utilizes the asymmetric multiquadric collocation method for spatial discretization, resulting in a system of ordinary differential equations (ODEs) in time. The fourth-order Runge-Kutta (RK) method is then applied to solve this system. The method is illustrated by solving selected problems and comparing the results to exact solutions, highlighting its effectiveness. The algorithm is user-friendly, accurate, and suitable for one-dimensional linear diffusion problems with complex initial and boundary conditions, offering a new perspective in computational physics and numerical analysis.