Numerical simulation based on meshless technique to study the biological population model

Abstract

A kind of spectral meshless radial point interpolation method is proposed to degenerate parabolic equations arising from the spatial diffusion of biological populations and satisfactory agreements is archived. This method is based on collocation methods with mesh-free techniques as a background. In contrast to the finite-element method and those meshless methods based on Galerkin weak form, such as element-free Galerkin, there is no integration tools in this approach. Furthermore, some numerical experiments are given to validate the accuracy of the results and stability of the present method.

Parameter estimation of some Kumaraswamy-G type distributions

“…For example, some recent simulation studies can be found in [1,18]. Abbasbandy and Shivanian [1] used numerical simulation based on meshless technique to study the biological population model.…”

“…For example, some recent simulation studies can be found in [1,18]. Abbasbandy and Shivanian [1] used numerical simulation based on meshless technique to study the biological population model. Vajargah and Shoghi [18] used quasi-Monte Carlo method in prediction of total index of stock market and value at risk.…”

Application of the SBA Method to Solve the Nonlinear Biological Population Models

“…The spatial diffusion of some biological species is described by nonlinear partial differential equations. In the last years, various numerical powerful methods have been applied to get the solutions of general degenerate parabolic equations, such as collocation methods with mesh-free technique [2], variational iteration method [10], Adomian decomposition method (ADM) [1,13], homotopy perturbation method [8,9], homotopy analysis Sumudu transform method [12], etc.…”

Local radial basis function interpolation method to simulate 2D fractional‐time convection‐diffusion‐reaction equations with error analysis

“…A. Shirzadi et al considered the same problem in both weak convection coefficients and convection dominant cases and applied meshless local Petrov‐Galerkin (MLPG) method to obtain better results but MLPG is time consuming as the result of determining shape parameter and calculating integration around each nodal point, the readers are referred to the Refs. to survey meshless methods. Z. J. Fu et al have considered the problem (1)–(4) and proposed Laplace transformed boundary particle method to solve it effectively.…”