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

Abstract

Purpose

This study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains.

Design/methodology/approach

The 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.

Findings

First, 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 O(τ1+γ) and O(τ2−γ) for 0 < γ < 1. Finally, some numerical examples have been presented to show the high accuracy and acceptable results of the proposed technique.

Originality/value

The proposed numerical technique is flexible for different computational domains.

Citation

Abbaszadeh, M., Pourbashash, H. and Khaksar-e Oshagh, M. (2022), "The local meshless collocation method for solving 2D fractional Klein-Kramers dynamics equation on irregular domains", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 1, pp. 41-61. https://doi.org/10.1108/HFF-12-2020-0781