Wright functions as scale-invariant solutions of the diffusion-wave equation
Journal of Computational and Applied Mathematics - Special issue on higher transcendental functions and their applications
Algorithm 368: Numerical inversion of Laplace transforms [D5]
Communications of the ACM
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
A Unified Framework for Numerically Inverting Laplace Transforms
INFORMS Journal on Computing
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics
Journal of Computational Physics
Implicit finite difference approximation for time fractional diffusion equations
Computers & Mathematics with Applications
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
Numerical inversion of 2-D Laplace transforms applied to fractional diffusion equations
Applied Numerical Mathematics
Least squares finite-element solution of a fractional order two-point boundary value problem
Computers & Mathematics with Applications
Fractional diffusion equations by the Kansa method
Computers & Mathematics with Applications
Numerical simulations of 2D fractional subdiffusion problems
Journal of Computational Physics
A direct O(Nlog2N) finite difference method for fractional diffusion equations
Journal of Computational Physics
High-order finite element methods for time-fractional partial differential equations
Journal of Computational and Applied Mathematics
An implicit RBF meshless approach for time fractional diffusion equations
Computational Mechanics
Computers & Mathematics with Applications
The BEM for numerical solution of partial fractional differential equations
Computers & Mathematics with Applications
Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
SIAM Journal on Scientific Computing
The asymptotics of the solutions to the anomalous diffusion equations
Computers & Mathematics with Applications
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This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.