Fast numerical algorithm for the reaction-diffusion equations using an interpolating method

We present a fast and splitting-based numerical scheme that employs an interpolation method for the system of the reaction-diffusion equations. Typically, the time step restriction arises to the nonlinear reaction terms when we calculate the highly stiff system of reaction-diffusion equations. This issue can be resolved through various implicit solvers, but they shall present another problem of having a longer computing time for each step. In order to overcome these shortcomings, we present a splitting-based hybrid scheme with a pre-iteration process before the main loop to derive interpolating points which are employed to evaluate the intermediate solution, instead of computing the nonlinear reaction term directly. The stability and convergence analysis are provided for selected reaction-diffusion models. We verify that the results of our proposed method are in good agreements with those in the references, as demonstrated numerically. Furthermore, we examine and compare the computing time performance among the methods, and draw that our proposed method yields good results.