A second-order accurate numerical method for the two-dimensional fractional diffusion equation

By Charles Tadjeran, Mark M. Meerschaert. Journal of Computational Physics, 2007

357 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/89ec4eced0c56852b7e9c3c136cd8a78cc5ff4e7

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Citations in the corpus

Local discontinuous Galerkin methods for fractional diffusion equations (2013, neutral): “Nevertheless, methods based on finite difference methods [23] and finite element formulations [10,11] have been developed and successfully applied.”
Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods (2008, methodology): “Numerical and analytical methods have included finite difference method [10]–[12], [29], Adomian decomposition method [1], [14]–[18], [23], variational iteration method [5], [19], [21], [24], homotopy perturbation method [20], [21], and generalized differential transform method [22], [25].”
Compact finite difference method for the fractional diffusion equation (2009, methodology): “Meerschaert and Tadjeran [4] studied the onedimensional radial flow model, they found that the fractional derivative describes more accurately the early arrival that cannot be explained by the classical advection–dispersion equations and they presented an implicit Euler method, based on a .”
Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation (2015, neutral): “, the finite difference method [11,12], reproducing kernel space method [13,14], Adams–Bashforth–Moulton method [15], homotopy perturbation method [16,17], Adomian decomposition method [18,19], homotopy analysis method [20,21], and generalized differential transform method [22,23].”
The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation (2013, methodology): “There are also numerical methods for high-dimensional fractional diffusion equations; see, for example, [8, 11, 35, 58, 63].”
On the numerical solutions for the fractional diffusion equation (2011, methodology): “The main idea of this work is to apply the Chebyshev collocation method to discretize (3) to get a linear system of ordinary differential equations thus greatly simplifying the problem, and use the finite difference method (FDM) ([8]-[10], [16]) to solve the resulting system.”
The homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian's decomposition method (2013, methodology): “These methods include the finite difference method [4–6], the Adams–Bashforth–Moulton method [7], the homotopy perturbation method (HPM) [8–10], the generalized differential transform method [11,12], the variational iteration method [13–15] and the Adomian’s decomposition method (ADM) [16,17].”