Boundary particle method for Laplace transformed time fractional diffusion equations

摘要：

This paper develops a novel boundary discretization meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. The present approach implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation and then employs a truly boundary-only meshless boundary particle method (BPM) to solve the Laplace-transformed inhomogeneous problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique is used to reduce an inhomogeneous problem to a series of higher-order homogeneous problems. Finally, the Stehfest numerical Laplace inversion can retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. The present method avoids enormous computing costs for the simulation of a long history fractional systems and remedies the low accuracy at the initial instants of time encountered in the other traditional methodologies. Numerical experiments demonstrate that the LTBPM is highly accurate, computationally efficient, and numerically stable for 2D and 3D time fractional diffusion equations.

关键词： Boundary particle method Laplace transform numerical inverse Laplace transform meshless time fractional derivative anomalous diffusion.

作者: Zhuo-Jia Fu Wen Chen Hai-Tian Yang

作者单位: College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing, Jiangsu 210098, P.R State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technolog

会议类型: 国际会议

会议名称: 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)

会议地点: 南京

会议语种:英文

页码: 1-19

在线出版日期: 2012-05-14（万方平台首次上网日期，不代表论文的发表时间）