Interpolating MLPG method to investigate predator-prey population dynamic with complex characters

The predator-prey model is a pair of first-order nonlinear differential equations which are used to explain the dynamics of biological systems. These systems contain two species interacting, one as a predator and the other as prey. This work proposes a meshless local Petrov-Galerkin (MLPG) method based upon the interpolating moving least squares (IMLS) approximation, for the numerical solution of the predator-prey systems. With this aim, the space derivative is discretized by the MLPG technique in which the test and trial functions are chosen from the shape functions of IMLS approximation. Next, a semi-implicit finite difference approach is utilized to discretize the time derivative. The main aim of this work is to bring forward a flexible numerical procedure to solve predator-prey systems on complicated geometries.