An implicit RBF meshless method for a fractal mobile/immobile transport model
Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.
fractal mobile/immobile transport model finite difference method meshless method
Q. Liu F. Liu I. Turner V. Anh Y.T. Gu
School of Mathematical Sciences, Xiamen UniversityXiamen 361005, China. Mathematical Sciences, Queensland University of TechnologyGPO Box 2434, Brisbane, Qld. 4001, Austral School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technolog, Brisban
国际会议
The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)
南京
英文
1-8
2012-05-14（万方平台首次上网日期，不代表论文的发表时间）