Hermite Collocation and SSPRK Schemes for the Numerical Treatment of a Generalized Kolmogorov-Petrovskii-Piskunov Equation

In this study we develop high order numerical methods to capture the spatiotemporal dynamics of a generalized Kolmogorov-Petrovskii-Piskunov (KPP) equation characterized by density dependent non-linear diffusion. Towards this direction we consider third order Strong Stability Preserving Runge-Kutta (SSPRK) temporal discretization schemes coupled with the fourth order Hermite cubic Collocation (HC) spatial discretization method. We numerically investigate their convergence properties to reveal efficient HC-RK pairs for the numerical treatment of the generalized KPP equation. The Hadamard product is used to characterize the collocation discretized non-linear equation terms. Several numerical experiments are included to demonstrate the performance of the methods.