Numerical analysis and fast implementation of a fourth-order difference scheme for two-dimensional space-fractional diffusion equations

DOI10.1016/j.amc.2018.10.057zbMath1429.65203OpenAlexW2899366972WikidataQ129020367 ScholiaQ129020367MaRDI QIDQ2008405

Zhiyong Xing, Liping Wen

Publication date: 25 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.10.057

zbMATH Keywords

conjugate gradient methodspace-fractional diffusion equationfast Fourier transform (FFT)quasi-compact difference scheme\(L_\infty \)-norm

Mathematics Subject Classification ID

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

Related Items (11)

A local RBFs-based DQ approximation for Riesz fractional derivatives and its applications ⋮ Implicit Runge-Kutta and spectral Galerkin methods for Riesz space fractional/distributed-order diffusion equation ⋮ An efficient fourth-order accurate conservative scheme for Riesz space fractional Schrödinger equation with wave operator ⋮ High-order time-stepping methods for two-dimensional Riesz fractional nonlinear reaction-diffusion equations ⋮ On \(\tau\)-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations ⋮ A fourth-order conservative difference scheme for the Riesz space-fractional sine-Gordon equations and its fast implementation ⋮ Fast direct solver for CN-ADI-FV scheme to two-dimensional Riesz space-fractional diffusion equations ⋮ An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional sine-Gordon equations ⋮ An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations ⋮ An efficient difference scheme for time-fractional KdV equation ⋮ Numerical framework for the Caputo time-fractional diffusion equation with fourth order derivative in space

Cites Work

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• A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients
• A new difference scheme for the time fractional diffusion equation
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes first problem for a heated generalized second grade fluid
• A fourth-order approximation of fractional derivatives with its applications
• Fractional cable equation models for anomalous electrodiffusion in nerve cells: Infinite domain solutions
• Fractional differential equations in electrochemistry
• Fractals and fractional calculus in continuum mechanics
• Waiting-times and returns in high-frequency financial data: An empirical study
• A fourth-order scheme for space fractional diffusion equations
• A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations
• Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
• A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
• Fourth Order Difference Approximations for Space Riemann-Liouville Derivatives Based on Weighted and Shifted Lubich Difference Operators
• The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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