A compact Fourth-Order Implicit-Explicit Runge-Kutta Type Method for Solving Diffusive Lotka–Volterra System

Abstract

This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme for spatial part combined with implicit-explicit Runge Kutta scheme in temporal are proposed. Furthermore, boundary points are discretized by using a compact finite difference scheme in terms of fourth order accuracy. A key idea for proposed scheme is to take full advantage of method of line (MOL), this is consequently enabling us to use implicit-explicit Runge Kutta method, that are of fourth order in time. We constructed fourth order accuracy in both space and time and is unconditionally stable. This is consequently leading to a reduction in the computational cost of the scheme. Numerical experiments show that the combination of the compact finite difference with IMEX- RK methods give an accurate and reliable for solving the Lotka-Volterra-diffusion.