High-Order Finite Difference Schemes for Solving the Advection-Diffusion Equation

Mathematical and Computational Applications

Sari, Murat¹ 

关键词: Advection-Diffusion Equation;    Contaminant Transport;    High-order Finite Difference Schemes;    Runge-Kutta;   

DOI  :  10.3390/mca15030449

学科分类：计算数学

来源: mdpi

【 摘 要 】

Up to tenth-order finite difference schemes are proposed in this paper to solve one-dimensional advection-diffusion equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order finite difference schemes in space and a fourth-order Runge-Kutta scheme in time have been combined. The methods are implemented to solve two problems having exact solutions. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the current methods. The techniques are seen to be very accurate in solving the advection-diffusion equation for Pe ≤ 5 . The produced results are also seen to be more accurate than some available results given in the literature.

【 授权许可】

CC BY