Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions

Authors:
Jincheng Ren;Zhi-Zhong Sun;Xuan Zhao
Affiliations:
Department of Mathematics, Southeast University, Nanjing 210096, PR China and Department of Mathematics, Shangqiu Normal University, Henan Shangqiu 476000, PR China;Department of Mathematics, Southeast University, Nanjing 210096, PR China;Department of Mathematics, Southeast University, Nanjing 210096, PR China
Venue:
Journal of Computational Physics
Year:
2013

Citing 21
Cited 4

An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations

SIAM Journal on Numerical Analysis
The accuracy and stability of an implicit solution method for the fractional diffusion equation

Journal of Computational Physics
Weighted average finite difference methods for fractional diffusion equations

Journal of Computational Physics
Numerical Approximation of a Time Dependent, Nonlinear, Space-Fractional Diffusion Equation

SIAM Journal on Numerical Analysis
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
Numerical algorithm for the time fractional Fokker-Planck equation

Journal of Computational Physics
New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation

SIAM Journal on Numerical Analysis
Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

Journal of Computational and Applied Mathematics
Compact finite difference method for the fractional diffusion equation

Journal of Computational Physics
A fully discrete difference scheme for a diffusion-wave system

Applied Numerical Mathematics
A Space-Time Spectral Method for the Time Fractional Diffusion Equation

SIAM Journal on Numerical Analysis
A compact finite difference scheme for the fractional sub-diffusion equations

Journal of Computational Physics
Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation

SIAM Journal on Scientific Computing
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions

Journal of Computational Physics
An implicit RBF meshless approach for time fractional diffusion equations

Computational Mechanics
Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion

Computers & Mathematics with Applications
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation

Journal of Computational Physics
Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions

SIAM Journal on Scientific Computing
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

The finite difference approximation for a class of fractional sub-diffusion equations on a space unbounded domain

Journal of Computational Physics
Numerical Algorithm With High Spatial Accuracy for the Fractional Diffusion-Wave Equation With Neumann Boundary Conditions

Journal of Scientific Computing
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

Quantified Score

Hi-index	31.46

Visualization

Abstract

An effective finite difference scheme is considered for solving the time fractional sub-diffusion equation with Neumann boundary conditions. A difference scheme combining the compact difference approach the spatial discretization and L"1 approximation for the Caputo fractional derivative is proposed and analyzed. Although the spatial approximation order at the Neumann boundary is one order lower than that for interior mesh points, the unconditional stability and the global convergence order O(@t^2^-^@a+h^4) in discrete L"2 norm of the compact difference scheme are proved rigorously, where @t is the temporal grid size and h is the spatial grid size. Numerical experiments are included to support the theoretical results, and comparison with the related works are presented to show the effectiveness of our method.