A Compact ADI Finite Difference Method for 2D Reaction-Diffusion Equations with Variable Diffusion Coefficients
Date
2023-08
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Abstract
Reaction-diffusion systems on a spatially heterogeneous domain have been widely used to model various biological applications. However, it is rarely possible to solve such partial differential equations (PDEs) analytically. Therefore, efficient and accurate numerical methods for solving such PDEs are desired. In this paper, we apply the well-known Pad\'{e} approximation-based operator splitting (ADI) scheme. The new scheme is compact and fourth-order accurate in space. Combined with the Richardson extrapolation, the method can be improved to fourth-order accurate in time. Stability analysis shows that the method is unconditionally stable; thus, a large time step can be used to improve the overall computational efficiency further, Numerical examples have also demonstrated the new scheme's high efficiency and high-order accuracy.
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He, M. (2023). A compact ADI finite difference method for 2D reaction-diffusion equations with variable diffusion coefficients (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.