A high-order compact difference method and its Richardson extrapolation for semi-linear reaction-diffusion equations with piecewise continuous argument in diffusion term

In this paper, for the initial-boundary value problems of semi-linear reaction-diffusion equations with piecewise continuous argument in spatial derivative, we suggest Crank-Nicolson method, high-order compact difference (HOCD) method and HOCDbased Richardson extrapolation (RHOCD) method. Under the appropriate conditions, it is proved that HOCD (resp. RHOCD) method has the computational accuracy O(& tau;2+h4) (resp. O(& tau;4+h4)). This shows that RHOCD method improves the calculation accuracy of HOCD method in temporal direction. Moreover, we also analyze the stability of HOCD method and thus derive a global stability criterion of this method. Finally, with a series of numerical experiments, we further confirm the computational effectiveness and theoretical accuracy of the concerned methods. & COPY; 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.