A Compact Finite Difference Scheme for Reaction-convection-diffusion Equation

• Main Authors: Jafar Biazar, Mohammad Bagher Mehrlatifan
• Format: บทความวารสาร
• Language: English
• Published: Science Faculty of Chiang Mai University 2019
• Online Access: http://it.science.cmu.ac.th/ejournal/dl.php?journal_id=9161; http://cmuir.cmu.ac.th/jspui/handle/6653943832/64123
• Institution: Chiang Mai University

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.