Simulation of predator–prey system with two-species, two chemicals and an additional chemotactic influence via direct meshless local Petrov–Galerkin method

Abstract

PurposeThis paper aims to introduce a new numerical approach based on the local weak form and the Petrov–Galerkin idea to numerically simulation of a predator–prey system with two-species, two chemicals and an additional chemotactic influence.Design/methodology/approachIn the first proceeding, the space derivatives are discretized by using the direct meshless local Petrov–Galerkin method. This generates a nonlinear algebraic system of equations. The mentioned system is solved by using the Broyden’s method which this technique is not related to compute the Jacobian matrix.FindingsThis current work tries to bring forward a trustworthy and flexible numerical algorithm to simulate the system of predator–prey on the nonrectangular geometries.Originality/valueThe proposed numerical results confirm that the numerical procedure has acceptable results for the system of partial differential equations.