Journal
COMPUTATIONAL MECHANICS
Volume 48, Issue 1, Pages 1-12Publisher
SPRINGER
DOI: 10.1007/s00466-011-0573-x
Keywords
Fractional differential equation; Time fractional diffusion equation; Meshless method; Radial basis function; Implicit numerical scheme
Funding
- NSF of Fujian [2010J01011, 2010J05009]
- Queensland International Fellowship fund
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This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.
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