Computational modeling of nonlinear reaction-diffusion Fisher–KPP equation with mixed modal discontinuous Galerkin scheme

Abstract

In this study, a mixed modal discontinuous Galerkin (DG) scheme is developed for solving the two-dimensional nonlinear Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher–KPP) reaction-diffusion equation emerging in biology sciences. This numerical scheme is based on the concept of addressing an additional auxiliary unknown in the high-order derivative diffusion term. The scaled Legendre polynomials with third-order accuracy are used for spatial discretization, while, an explicit Strongly Stability Preserving Runge-Kutta scheme with third-order accuracy is adopted for the temporal discretization. This numerical approach is widely applicable for several nonlinear reaction-diffusion problems. To verify the accuracy and reliability of the DG scheme, several well-known numerical problems in literature are solved. The derived numerical solutions and errors show that the results are in good agreement with the exact solutions. This proposed DG approach demonstrates that it is an efficient technique for finding numerical solutions for a wide range of linear and nonlinear physical models.