Application of Meshfree Method Based on Compactly Supported Radial Basis Function for Solving Unsteady Isothermal Gas Through a Micro–Nano Porous Medium

Abstract

In this paper, we have applied the Meshless method based compactly supported radial basis function collocation for obtaining the numerical solution of unsteady gas equation. The unsteady gas equation is a second order non-linear two-point boundary value ordinary differential equation on the semi-infinite domain, with a boundary condition in the infinite. The compactly supported radial basis function collocation method reduces the solution of the equation to the solution of a system of algebraic equation. also, we compare the results of this work with some results. It is found that our results agree well with those by the numerical method, which verifies the validity of the present work.

Numerical investigation of Differential Biological Models via RBF collocation Method with Genetic Strategy

“…They enlarged a Lagrangian method according to Kernel estimate method [24]. A number of meshfree methods such as smoothing particle hydrodynamic (SPH) [11,64], Element-Free Galerkin (EFG) [8,39], Reproducing Kernel method (RKM) [1,7], Meshless local Petrov-Galerkin (MLPG) [5,55], Comapctly supported radial basis function method(CSRBF) [48,49], Radial basis function differential quadrature method(RBF-DQ) [47,63] and Kansa method (KM) [51,61] are used for solving differential equations (DEs). The appearance of meshfree methods was through the difficulty of the classic methods such as Finite Element method (FEM) [31,65] and Finite Difference method (FDM) [14,15] which require a mesh of points for solving problems.…”