Local radial basis function-finite difference based algorithms for singularly perturbed Burgers’ model

Abstract

This work analyzes singularly perturbed Burgers’ model by developing two meshfree algorithms based on local radial basis function-finite difference approximation. The main goal of this task is to present computational modeling of the model when perturbation parameter ɛ→0 where most of the traditional numerical methods fail. In the evolvement of the first algorithm, time derivative is discretized by forward finite difference and then truncation error, stability and convergence analysis are discussed for the semi-discrete model. After that, local radial basis function-finite difference approximation is used for spatial discretization. In the second numerical algorithm, local radial basis function-finite difference and RK4 method are applied for spatial and fully discretization respectively. Also, the stability of the scheme is discussed via matrix method.