The local meshless collocation method for solving 2D fractional Klein-Kramers dynamics equation on irregular domains

Abstract

PurposeThis study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains.Design/methodology/approachThe main aim of the current paper is to propose a local meshless collocation method to solve the two-dimensional Klein-Kramers equation with a fractional derivative in the Riemann-Liouville sense, in the time term. This equation describes the sub-diffusion in the presence of an external force field in phase space.FindingsFirst, the authors use two finite difference schemes to discrete temporal variables and then the radial basis function-differential quadrature method has been used to estimate the spatial direction. To discrete the time-variable, the authors use two different strategies with convergence orders and for 0 < γ < 1. Finally, some numerical examples have been presented to show the high accuracy and acceptable results of the proposed technique.Originality/valueThe proposed numerical technique is flexible for different computational domains.