Abstract
Reaction–diffusion systems on a spatially heterogeneous domain have been widely used to model various biological applications. However, solving such partial differential equations (PDEs) analytically is rarely possible. Therefore, efficient and accurate numerical methods for solving such PDEs are desired. In this paper, we apply the well-known Padé approximation-based operator splitting techniques and develop a fourth-order compact alternative directional implicit (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 accuracy 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. Numerical examples have also demonstrated the new scheme’s high efficiency and high order accuracy.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
