Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
From MaRDI portal
Publication:5254144
DOI10.1137/130933447zbMath1318.65048arXiv1304.7425OpenAlexW2057119166MaRDI QIDQ5254144
Publication date: 9 June 2015
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1304.7425
stabilityconvergencenumerical examplestruncation errorfractional diffusion equationweighted and shifted Lubich difference operators
Heat equation (35K05) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)
Related Items (only showing first 100 items - show all)
The upwind PPM scheme and analysis for solving two-sided space-fractional advection-diffusion equations in three dimension ⋮ Preconditioned fourth-order exponential integrator for two-dimensional nonlinear fractional Ginzburg-Landau equation ⋮ The characteristic difference DDM for solving the time-fractional order convection-diffusion equations ⋮ Analysis and efficient implementation of alternating direction implicit finite volume method for Riesz space‐fractional diffusion equations in two space dimensions ⋮ A linear decoupled physical-property-preserving difference method for fractional-order generalized Zakharov system ⋮ Analysis of (shifted) piecewise quadratic polynomial collocation for nonlocal diffusion model ⋮ An efficient compact difference-proper orthogonal decomposition algorithm for fractional viscoelastic plate vibration model ⋮ A fast time two-mesh finite volume element algorithm for the nonlinear time-fractional coupled diffusion model ⋮ The construction of an optimal fourth-order fractional-compact-type numerical differential formula of the Riesz derivative and its application ⋮ On \(\tau\)-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations ⋮ Local discontinuous Galerkin methods with novel basis for fractional diffusion equations with non-smooth solutions ⋮ High order finite difference methods on non-uniform meshes for space fractional operators ⋮ Numerical methods for nonlocal and fractional models ⋮ Point-wise error estimate of a conservative difference scheme for the fractional Schrödinger equation ⋮ Stability and convergence of the Crank-Nicolson scheme for a class of variable-coefficient tempered fractional diffusion equations ⋮ Numerical algorithms for the time-space tempered fractional Fokker-Planck equation ⋮ Stability and convergence analysis of finite difference schemes for time-dependent space-fractional diffusion equations with variable diffusion coefficients ⋮ Numerical analysis for compact difference scheme of fractional viscoelastic beam vibration models ⋮ A class of unconditioned stable 4-point WSGD schemes and fast iteration methods for space fractional diffusion equations ⋮ A series of high-order quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives ⋮ Estimation of the smallest eigenvalue in fractional escape problems: semi-analytics and fits ⋮ Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy ⋮ Models of space-fractional diffusion: a critical review ⋮ High order algorithm for the time-tempered fractional Feynman-Kac equation ⋮ High-order compact difference methods for Caputo-type variable coefficient fractional sub-diffusion equations in conservative form ⋮ Efficient preconditioners for Radau-IIA time discretization of space fractional diffusion equations ⋮ An \textit{a posteriori} Fourier regularization method for identifying the unknown source of the space-fractional diffusion equation ⋮ Implicit Runge-Kutta and spectral Galerkin methods for Riesz space fractional/distributed-order diffusion equation ⋮ Novel finite point approach for solving time-fractional convection-dominated diffusion equations ⋮ Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations ⋮ Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem ⋮ Numerical solution of space fractional diffusion equation by spline method combined with Richardson extrapolation ⋮ Approximating the Basset force by optimizing the method of van Hinsberg et al. ⋮ Fourth order compact scheme for space fractional advection-diffusion reaction equations with variable coefficients ⋮ Correction of high-order \(L_k\) approximation for subdiffusion ⋮ An \(h\)-\(p\) version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functions ⋮ A \(\tau \)-preconditioner for a non-symmetric linear system arising from multi-dimensional Riemann-Liouville fractional diffusion equation ⋮ An implicit difference scheme with the KPS preconditioner for two-dimensional time-space fractional convection-diffusion equations ⋮ Convergence Analysis of a Multigrid Method for a Nonlocal Model ⋮ An efficient conservative splitting characteristic difference method for solving 2-d space-fractional advection-diffusion equations ⋮ A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation ⋮ Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain ⋮ High-order numerical algorithms for Riesz derivatives via constructing new generating functions ⋮ Fast solution methods for Riesz space fractional diffusion equations with non-separable coefficients ⋮ The conservative characteristic difference method and analysis for solving two-sided space-fractional advection-diffusion equations ⋮ A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations ⋮ Multilevel Circulant Preconditioner for High-Dimensional Fractional Diffusion Equations ⋮ Approximation methods for solving fractional equations ⋮ Fourth-order compact difference schemes for the Riemann-Liouville and Riesz derivatives ⋮ Time fourth-order energy-preserving AVF finite difference method for nonlinear space-fractional wave equations ⋮ On a second order scheme for space fractional diffusion equations with variable coefficients ⋮ A fourth-order conservative difference scheme for the Riesz space-fractional sine-Gordon equations and its fast implementation ⋮ New fractional pseudospectral methods with accurate convergence rates for fractional differential equations ⋮ A fast second-order accurate method for a two-sided space-fractional diffusion equation with variable coefficients ⋮ Energy estimates for two-dimensional space-Riesz fractional wave equation ⋮ Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman-Kac equation ⋮ Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview ⋮ Asymptotic expansions and approximations for the Caputo derivative ⋮ Backward difference formulae and spectral Galerkin methods for the Riesz space fractional diffusion equation ⋮ Kronecker product based preconditioners for boundary value method discretizations of space fractional diffusion equations ⋮ An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional sine-Gordon equations ⋮ Parallel-in-time multigrid for space-time finite element approximations of two-dimensional space-fractional diffusion equations ⋮ A high-order difference scheme for the fractional sub-diffusion equation ⋮ Split-step alternating direction implicit difference scheme for the fractional Schrödinger equation in two dimensions ⋮ Compact difference scheme for a class of fractional-in-space nonlinear damped wave equations in two space dimensions ⋮ Fourth order finite difference schemes for time-space fractional sub-diffusion equations ⋮ A note on the stability of a second order finite difference scheme for space fractional diffusion equations ⋮ Numerical analysis and fast implementation of a fourth-order difference scheme for two-dimensional space-fractional diffusion equations ⋮ An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations ⋮ Finite difference approximation of space-fractional diffusion problems: the matrix transformation method ⋮ Fractional diffusion on bounded domains ⋮ Stability and convergence of finite difference method for two-sided space-fractional diffusion equations ⋮ Efficient preconditioner of one-sided space fractional diffusion equation ⋮ An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation ⋮ Spectral element method with geometric mesh for two-sided fractional differential equations ⋮ Backward difference formulae: the energy technique for subdiffusion equation ⋮ General linear and spectral Galerkin methods for the Riesz space fractional diffusion equation ⋮ A High Order Finite Difference Method for Tempered Fractional Diffusion Equations with Applications to the CGMY Model ⋮ A fourth-order approximation of fractional derivatives with its applications ⋮ An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation ⋮ Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients ⋮ A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative ⋮ Numerical methods for solving space fractional partial differential equations using Hadamard finite-part integral approach ⋮ Finite difference schemes for two-dimensional time-space fractional differential equations ⋮ A class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrödinger equations ⋮ An efficient second-order convergent scheme for one-side space fractional diffusion equations with variable coefficients ⋮ A second-order accurate scheme for two-dimensional space fractional diffusion equations with time Caputo-Fabrizio fractional derivative ⋮ Space-time finite element method for the distributed-order time fractional reaction diffusion equations ⋮ Preface: Numerical analysis of fractional differential equations ⋮ Fast algorithms for high-order numerical methods for space-fractional diffusion equations ⋮ High-order central difference scheme for Caputo fractional derivative ⋮ Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions ⋮ Boundary conditions for two-sided fractional diffusion ⋮ A fourth-order scheme for space fractional diffusion equations ⋮ An explicit form for higher order approximations of fractional derivatives ⋮ Finite element method for two-sided fractional differential equations with variable coefficients: Galerkin approach ⋮ Crank--Nicolson Alternative Direction Implicit Method for Space-Fractional Diffusion Equations with Nonseparable Coefficients ⋮ Dissipativity and Contractivity Analysis for Fractional Functional Differential Equations and their Numerical Approximations ⋮ On \(\tau\) matrix-based approximate inverse preconditioning technique for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations ⋮ Fast and high-order accuracy numerical methods for time-dependent nonlocal problems in \(\mathbb{R}^2\)
This page was built for publication: Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
