Numerical Simulation of One-Dimensional Advection Diffusion Equation by New Hybrid Explicit Finite Difference Schemes

Abstract

In this paper, the aim is to develop two Hybrid Explicit Schemes based on the Finite Difference method for a one- dimensional Advection Diffusion Equation. Moreover, the study considered the advection-diffusion equation as an initial boundary value problem (IBVP) for numerical solutions obtained from various second-order explicit methods along with the solution by proposed methods. Von-Neumann stability analysis is used to analyze the stability of the developed schemes graphically. In the numerical analysis of errors, the L 2 has been computed to compare proposed methods with existing methods in literature and has been carried out in different conditions and step sizes. Proposed methods are robust explicit methods for the purpose of solution of the 1-D advection-diffusion equation.