Study of the growth ratio of genetic communities using a new meshless method

‎In recent decades researchers introduced many numerical methods for solving partial differential equations. Some of these methods have limitations in solving problems with complex domains because of the need to construct meshes. Therefore, scientists developed a new set of numerical methods called meshless methods. In this paper, we introduce the direct meshless local Petrov-Galerkin method to the numerical study of the nonlinear two-dimensional Fisher equation. This method is based on the local weak form of the equation and uses the generalized moving least square method to approximate the unknown function. To show the efficiency and capability of the method, we report the numerical results in regular and irregular domains with a uniform and scattered distribution of nodes. Comparison of the obtained results with other methods indicates the accuracy and efficiency of this method.