Radial basis functions based meshfree schemes for the simulation of non-linear extended Fisher–Kolmogorov model

Abstract

This work offers two radial basis functions (RBFs) based meshfree schemes for the numerical simulation of non-linear extended Fisher–Kolmogorov model. In the development of the first scheme, first of all, time derivative is discretized by forward finite difference and then stability and convergence of the semi-discrete model is analyzed in L2 and H02 spaces. After that, RBF-differential quadrature method (RBF–DQM) is applied for fully discretization. Then, the obtained system of algebraic linear equations is solved by Gauss-elimination method. In the second numerical scheme, first RBF–DQM is applied for spatial derivatives approximation and then we obtained a system of nonlinear ODEs. After that, the system of ODEs is solved by RK4 Method. Also, the stability of the scheme is discussed via matrix method. In order to prove the meshfree property of the proposed methods, we considered non-uniform angular and rectangular domains with different radius. In the supporting domain, we used 5,10,15,20 and 25 supporting nodes for each nodes. Six instances of the model are considered to examine the reliability and chastity of the proposed schemes and found accurate results.