A Compact Finite Difference Scheme for Reaction-convection-diffusion Equation
Jafar Biazar and Mohammad Bagher Mehrlatifan** Author for corresponding; e-mail address: biazar@guilan.ac.ir; mehrlatifan@gmail.com
Volume: Vol.45 No.3 (May 2018)
Research Article
DOI:
Received: 26 May 2016, Revised: -, Accepted: 7 March 2017, Published: -
Citation: Biazar J. and Mehrlatifan M.B., A Compact Finite Difference Scheme for Reaction-convection-diffusion Equation, Chiang Mai Journal of Science, 2018; 45(3): 1559-1568.
Abstract
In this paper, a new method is developed for approximating solution to the reaction-convection-diffusion equation, in which reaction rate and diffusion coefficient are small parameters. A compact finite difference scheme (CFD) is applied for discretizing spatial derivatives of linear reaction-convection-diffusion equation, which leads to a linear system of ordinary differential equations. To solve the resulted system, the cubic C1-spline collocation method is applied. The accuracy in space and time is of fourth-order i.e. O(h4, k4). Although the proposed scheme is not A-stable, it is shown to be unconditionally stable. Numerical results show that the combination of the compact finite difference approximation and the cubic C1-spline collocation methods give an efficient method for solving the reaction-convection-diffusion equation.