Numerical Solution of the Advection-Diffusion Equation Using the Radial Basis Function

Abstract

The advection-diffusion equation is a form of partial differential equation. This equation is also known as the transport equation. The purpose of this research is to approximatio the solution of advection-diffusion equation by numerical approach using radial basis functions network. The approximation is performed by using the multiquadrics basis function. The simulation of the numerical solution is run with the help of the Matlab program. The one-dimensional advection-diffusion equation used is ∂u/∂t+C ∂u/∂x=D (∂^2 u)/(∂x^2 ) with given initial conditions, boundary conditions, and exact solution u(x,t). The numerical solution approximation using the radial basis function network with dt=0.004 and dx=0.02 produces the value at each discretization point is close to the exact solution. In this study, the smallest error between numerical solution and the exact solution is obtained 2.18339 ×〖10〗^(-10).

Keywords

• advection-diffusion equation
• numerical solution
• pde
• radial basis function.