The accuracy and stability of an implicit solution method for the fractional diffusion equation
By T. Langlands, B. Henry. 2005
572 citations recorded by the source corpus.
Subfields: Modeling and Simulation, Numerical Analysis, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/e9c2fdbaaf51428957fffd22903e7a7bb40bdbe3
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In Modeling and Simulation
- Fawang Liu
- Ian L Turner
- Changpin Li
- Vo Anh
- Mingrong Cui
- Fanhai Zeng
- Mark M. Meerschaert
- Pinghui Zhuang
In Numerical Analysis
- Fawang Liu
- Changpin Li
- Ian L Turner
- Vo Anh
- Mingrong Cui
- Fanhai Zeng
- Pinghui Zhuang
- Mark M. Meerschaert
In Public Health, Environmental and Occupational Health
- 许传炬
- Ian L Turner
- Mark Ainsworth
- William McLean
- Fanhai Zeng
- G. Em Karniadakis
- Mingrong Cui
- Xianjuan Li
Citations in the corpus
- Compact finite difference method for the fractional diffusion equation (2009, background): “[5] T.A.M. Langlands, B.I. Henry, The accuracy and stability of an implicit solution method for the fractional diffusion equation, J. Comput.”
- Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem (2013, methodology): “The existing numerical methods includes finite difference [7,11,19], Galerkin finite element [4, 5, 15], finite difference/spectral method [9], time-space spectral method [8], and so on.”
- The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation (2013, methodology): “The numerical methods for the subdiffusion equation with Neumann boundary conditions were presented in [24, 47, 60], in which the L1 method is used to approximate the time fractional derivative.”
- Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations (2015, unknown): “1) One of the popular schemes of discretizing the Caputo fractional derivative is the so-called L1 approximation [17, 18, 19, 32, 34, 38, 39, 52], which is simply based on the piecewise linear interpolation of u on each subinterval.”
- A finite element method for time fractional partial differential equations (2011, background): “[18] T.A.M. Langlands and B.I. Henry, The accuracy and stability of an implicit solution method for the fractional diffusion equation.”
- A unified Petrov-Galerkin spectral method for fractional PDEs (2015, methodology): “Finally, we formulate a general fast linear solver based on the eigenpairs of the corresponding temporal and spatial mass matrices with respect to the stiffness matrices, which reduces the computational cost drastically.”
- A Fourier method for the fractional diffusion equation describing sub-diffusion (2007, methodology): “Langlands and Henry [13] have investigated this problem.”