Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation
Numerical Algorithms
Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
SIAM Journal on Scientific Computing
High-order finite element methods for time-fractional partial differential equations
Journal of Computational and Applied Mathematics
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Numerical analysis and physical simulations for the time fractional radial diffusion equation
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Implicit difference approximation for the time fractional heat equation with the nonlocal condition
Applied Numerical Mathematics
Compact alternating direction implicit method for two-dimensional time fractional diffusion equation
Journal of Computational Physics
Error Estimates of Crank-Nicolson-Type Difference Schemes for the Subdiffusion Equation
SIAM Journal on Numerical Analysis
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Journal of Scientific Computing
A high-order compact exponential scheme for the fractional convection-diffusion equation
Journal of Computational and Applied Mathematics
Numerical simulation of the fractional Bloch equations
Journal of Computational and Applied Mathematics
Orthogonal spline collocation methods for the subdiffusion equation
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Two finite difference schemes for time fractional diffusion-wave equation
Numerical Algorithms
Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
Journal of Scientific Computing
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A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous subdiffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and convergence of the INM are investigated by the energy method. Some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and supporting theoretical results can also be applied to other fractional integro-differential equations and higher-dimensional problems.