SIAM Journal on Numerical Analysis
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
A second-order accurate numerical approximation for the fractional diffusion equation
Journal of Computational Physics
Weighted average finite difference methods for fractional diffusion equations
Journal of Computational Physics
Journal of Computational Physics
Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation
Journal of Computational and Applied Mathematics
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
SIAM Journal on Numerical Analysis
Numerical solutions for fractional reaction-diffusion equations
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Computers & Mathematics with Applications
Alternating direction implicit schemes for the two-dimensional fractional sub-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
Computers & Mathematics with Applications
Convergence analysis of moving finite element methods for space fractional differential equations
Journal of Computational and Applied Mathematics
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Stable multi-domain spectral penalty methods for fractional partial differential equations
Journal of Computational Physics
Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
Journal of Scientific Computing
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In this paper, we consider a variable-order anomalous subdiffusion equation. A numerical scheme with first order temporal accuracy and fourth order spatial accuracy for the equation is proposed. The convergence, stability, and solvability of the numerical scheme are discussed via the technique of Fourier analysis. Another improved numerical scheme with second order temporal accuracy and fourth order spatial accuracy is also proposed. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.