Stability and convergence analysis of finite difference schemes for time-dependent space-fractional diffusion equations with variable diffusion coefficients

DOI10.1007/s10915-017-0581-xzbMath1398.65214OpenAlexW2766915832MaRDI QIDQ1635891

Hai-Wei Sun, Xue-Lei Lin, Michael Kwok-Po Ng

Publication date: 1 June 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-017-0581-x

zbMATH Keywords

stabilityconvergencehigh-order finite difference schemestime-dependent space-fractional diffusion equationvariable diffusion coefficients

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11)

Related Items

Numerical method for system of space-fractional equations of superdiffusion type with delay and Neumann boundary conditions ⋮ A class of unconditioned stable 4-point WSGD schemes and fast iteration methods for space fractional diffusion equations ⋮ Space-fractional diffusion equation with variable coefficients: well-posedness and Fourier pseudospectral approximation ⋮ A finite difference method for space fractional differential equations with variable diffusivity coefficient ⋮ A conservative difference scheme with optimal pointwise error estimates for two‐dimensional space fractional nonlinear Schrödinger equations ⋮ A fast implicit difference scheme for solving the generalized time–space fractional diffusion equations with variable coefficients ⋮ A fast solver for multidimensional time-space fractional diffusion equation with variable coefficients ⋮ Fast solution methods for Riesz space fractional diffusion equations with non-separable coefficients ⋮ Approximation methods for solving fractional equations ⋮ A finite volume method for two-dimensional Riemann-Liouville space-fractional diffusion equation and its efficient implementation ⋮ Stability and convergence of finite difference method for two-sided space-fractional diffusion equations ⋮ Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients ⋮ An efficient second-order convergent scheme for one-side space fractional diffusion equations with variable coefficients ⋮ Crank--Nicolson Alternative Direction Implicit Method for Space-Fractional Diffusion Equations with Nonseparable Coefficients ⋮ Efficient ADI schemes and preconditioning for a class of high-dimensional spatial fractional diffusion equations with variable diffusion coefficients ⋮ An approximate inverse preconditioner for spatial fractional diffusion equations with piecewise continuous coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• A meshless method based on point interpolation method (PIM) for the space fractional diffusion equation
• Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
• A fourth-order approximation of fractional derivatives with its applications
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations
• Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
• High-order numerical algorithms for Riesz derivatives via constructing new generating functions
• Solution for a fractional diffusion-wave equation defined in a bounded domain
• Finite difference approximations for fractional advection-dispersion flow equations
• A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
• A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
• Finite difference approximations for two-sided space-fractional partial differential equations
• Superlinearly convergent algorithms for the two-dimensional space-time Caputo-Riesz fractional diffusion equation
• High-order algorithm for the two-dimension Riesz space-fractional diffusion equation
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• Fast algorithms for high-order numerical methods for space-fractional diffusion equations
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• A class of second order difference approximations for solving space fractional diffusion equations
• Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Stability and convergence analysis of finite difference schemes for time-dependent space-fractional diffusion equations with variable diffusion coefficients