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

Partial differential equations with variable coefficients involving discontinuous case play an important part in engineering, physics and ecology. In this paper, we will study nonlinear partial differential equations with variable coefficients arised from population models. Generally speaking, it is hard 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 invariants for differential equations. We will design the numerical schemes that preserve energy property and give conjectures for our target equation.