Numerical Solution of Advection-Diffusion Equation Using Meshless Method of Lines

In this paper, we present a meshless method of lines to solve one-dimensional advection-diffusion equation. For this aim, we use radial basis functions for approximate derivatives in space and fourth order Runge-Kutta scheme to solve the gained system of ordinary differential equations. Here, we use different types of radial basis functions such as multiquadric, Gaussian, inverse quadric and inverse multiquadric. The accuracy and applicability of this method are verified through the various examples. Our study shows that this method is very simple and can be easily used for solution of time-dependent partial differential equations.