The finite difference method for Caputo-type parabolic equation with fractional Laplacian: more than one space dimension

DOI10.1080/00207160.2017.1378810OpenAlexW2754675081MaRDI QIDQ5026499

Ye Hu, Changpin Li, Hefeng Li

Publication date: 8 February 2022

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

Full work available at URL: https://doi.org/10.1080/00207160.2017.1378810

zbMATH Keywords

stabilityconvergencefinite difference methodCaputo derivativefractional LaplacianCaffarelli-Silvestre extension

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods applied to problems in solid mechanics (74S20) Fractional partial differential equations (35R11)

Related Items

A speculative extension of the differential operator definition to fractal via the fundamental solution ⋮ Solving fractional Laplacian visco-acoustic wave equations on complex-geometry domains using Grünwald-formula based radial basis collocation method ⋮ Efficient Algorithms for Computing Multidimensional Integral Fractional Laplacians via Spherical Means ⋮ Predictor-corrector schemes for nonlinear space-fractional parabolic PDEs with time-dependent boundary conditions ⋮ Asymptotic behaviors of solution to partial differential equation with Caputo-Hadamard derivative and fractional Laplacian: hyperbolic case ⋮ On a conservative Fourier spectral Galerkin method for cubic nonlinear Schrödinger equation with fractional Laplacian ⋮ Parallel algorithms for nonlinear time-space fractional parabolic PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
• Hitchhiker's guide to the fractional Sobolev spaces
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations
• The finite difference method for Caputo-type parabolic equation with fractional Laplacian: one-dimension case
• Finite difference method for a fractional porous medium equation
• A PDE approach to fractional diffusion in general domains: a priori error analysis
• Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• A PDE Approach to Space-Time Fractional Parabolic Problems
• A concave—convex elliptic problem involving the fractional Laplacian
• Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations
• Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
• The Finite Difference Methods for Fractional Ordinary Differential Equations
• Fractional differentiation matrices with applications
• Numerical approximation of fractional powers of elliptic operators
• An Extension Problem Related to the Fractional Laplacian
• Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions