New two-derivative implicit-explicit Runge-Kutta methods for stiff reaction-diffusion systems

Abstract

Reaction-diffusion systems are extensively used in the mathematical modeling of biological and chemical systems to explain the Turing instability. Generally, reaction-diffusion systems are highly stiff in both reaction and diffusion terms. This paper discusses a new class of two-derivative implicit-explicit (IMEX) Runge-Kutta (RK) type methods for the numerical simulations of stiff reaction-diffusion systems. The present methods do not require numerical inversion of the coefficient matrix - computationally explicit. Stability properties of the developed methods are compared with the similar methods discussed in the literature. Moreover, accuracy and efficiency of the developed methods are validated by numerical simulations of spatiotemporal pattern formations for different reaction-diffusion systems, such as, phase-separation, Schnakenberg model and electrodeposition process.