Numerical simulation for a nonlinear partial differential equation with variable coefficients by means of the discrete variational derivative method

Partial differential equations with possibly discontinuous coefficients play an important part in engineering, physics and ecology. In this paper, we will study nonlinear partial differential equations with variable coefficients arising from population models. Generally speaking, it is difficult to analyze the behavior of nonlinear partial differential equations; therefore, we usually rely on the numerical approximation. Currently, there is an increasing interest in designing numerical schemes that preserve energy properties for differential equations. We will design the numerical schemes that preserve discrete energy property and show numerical experiments for a nonlinear partial differential equation with variable coefficients.