Adaptive parameter scheme in solving one-dimensional advection-diffusion equation including a variable source term

Abstract

Adaptive parameter scheme is proposed in the present investigation which is will pertinent to the problem of one-dimensional advection-diffusion equation including a variable source term. The adaptive parameter, truncation error, and correction term have been derive|d with respect to higher-order approximation. As the local Peclet number is a constant, the optimum value of this adaptive parameter can be easily acquired by exact solution. It is found thaj the incorporation of correction term which is produced due to the existence of variable source term can obtain very accurate results.

Keywords:

• Adaptive parameter scheme
• advection-diffusion equation
• truncation error
• correction term
• generalized finite difference formula

C.R. Categories::

• G.1.7
• J.2