An extrapolated finite difference method for two-dimensional fractional boundary value problems with non-smooth solution

DOI10.1080/00207160.2021.1907356OpenAlexW3137238146MaRDI QIDQ5063451

Shengyue Li, Wan-Rong Cao, Zhao-peng Hao

Publication date: 21 March 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2021.1907356

zbMATH Keywords

convergence ratelow regularityerror estimate in maximum normspatial fractional derivativenumerical correction

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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) Numerical methods for discrete and fast Fourier transforms (65T50) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Numerical analysis (65-XX)

Related Items (2)

High-order schemes based on extrapolation for semilinear fractional differential equation ⋮ Unconditionally stable and convergent difference scheme for superdiffusion with extrapolation

Cites Work

• Unnamed Item
• High order finite difference methods on non-uniform meshes for space fractional operators
• Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
• A finite difference scheme for semilinear space-fractional diffusion equations with time delay
• A fourth-order approximation of fractional derivatives with its applications
• A second-order accurate numerical method for a fractional wave equation
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Reproducing kernel particle method for two-dimensional time-space fractional diffusion equations in irregular domains
• An improved algorithm based on finite difference schemes for fractional boundary value problems with nonsmooth solution
• Finite difference approximations for fractional advection-dispersion flow equations
• Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation
• Fast algorithm based on TT-M FE system for space fractional Allen-Cahn equations with smooth and non-smooth solutions
• Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity
• Sharp error estimate of a compact \(L1\)-ADI scheme for the two-dimensional time-fractional integro-differential equation with singular kernels
• A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation
• Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions
• A high-order algorithm for time-Caputo-tempered partial differential equation with Riesz derivatives in two spatial dimensions
• A fast finite volume method for conservative space-fractional diffusion equations in convex domains
• A finite difference method with non-uniform timesteps for fractional diffusion equations
• Fast iterative method with a second-order implicit difference scheme for time-space fractional convection-diffusion equation
• A second-order accurate numerical approximation for the fractional diffusion equation
• Finite difference approximations for two-sided space-fractional partial differential equations
• An analysis of the Grünwald-Letnikov scheme for initial-value problems with weakly singular solutions
• Generalized Jacobi functions and their applications to fractional differential equations
• Implicit-Explicit Difference Schemes for Nonlinear Fractional Differential Equations with Nonsmooth Solutions
• Discretized Fractional Calculus
• A Finite Element Method with Singularity Reconstruction for Fractional Boundary Value Problems
• A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
• Numerical Algorithms for Time-Fractional Subdiffusion Equation with Second-Order Accuracy
• A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels
• Superconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave 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
• Existence and Uniqueness of the Weak Solution of the Space-time Fractional Diffusion Equation and a Spectral Method Approximation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Numerical Approximation of a Time Dependent, Nonlinear, Space‐Fractional Diffusion Equation
• Fractional Spectral Collocation Method

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