A fourth-order approximation of fractional derivatives with its applications

From MaRDI portal
Publication:728811

DOI10.1016/j.jcp.2014.10.053zbMath1352.65238OpenAlexW2068610405MaRDI QIDQ728811

Zhao-peng Hao, Zhi-zhong Sun, Wan-Rong Cao

Publication date: 20 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2014.10.053




Related Items (only showing first 100 items - show all)

Fourth-order alternating direction implicit difference scheme to simulate the space-time Riesz tempered fractional diffusion equationA high-order numerical algorithm for two-dimensional time-space tempered fractional diffusion-wave equationError estimate for indirect spectral approximation of optimal control problem governed by fractional diffusion equation with variable diffusivity coefficientSymbol-based preconditioning for Riesz distributed-order space-fractional diffusion equationsFractional centered difference scheme for high-dimensional integral fractional LaplacianA high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivativesHigh order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivativesImplicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditionsPoint-wise error estimate of a conservative difference scheme for the fractional Schrödinger equationA circulant preconditioner for the Riesz distributed-order space-fractional diffusion equationsThe construction of higher-order numerical approximation formula for Riesz derivative and its application to nonlinear fractional differential equations (I)A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equationsStability and convergence analysis of finite difference schemes for time-dependent space-fractional diffusion equations with variable diffusion coefficientsA class of unconditioned stable 4-point WSGD schemes and fast iteration methods for space fractional diffusion equationsAn extrapolated finite difference method for two-dimensional fractional boundary value problems with non-smooth solutionPreconditioners with symmetrized techniques for space fractional Cahn-Hilliard equationsA high-order predictor-corrector method for solving nonlinear differential equations of fractional orderFast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategyHigh order algorithm for the time-tempered fractional Feynman-Kac equationFourth-order numerical method for the space-time tempered fractional diffusion-wave equationNew explicit and accelerated techniques for solving fractional order differential equationsFast iterative method with a second-order implicit difference scheme for time-space fractional convection-diffusion equationPreconditioned quasi-compact boundary value methods for space-fractional diffusion equationsSpectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion EquationsFourth-order numerical method for the Riesz space fractional diffusion equation with a nonlinear source termAn improved algorithm based on finite difference schemes for fractional boundary value problems with nonsmooth solutionA multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equationsFourth order compact scheme for space fractional advection-diffusion reaction equations with variable coefficientsA \(\tau \)-preconditioner for a non-symmetric linear system arising from multi-dimensional Riemann-Liouville fractional diffusion equationAn implicit difference scheme with the KPS preconditioner for two-dimensional time-space fractional convection-diffusion equationsTwo novel energy dissipative difference schemes for the strongly coupled nonlinear space fractional wave equations with dampingA linearized high-order difference scheme for the fractional Ginzburg-Landau equationA Legendre spectral-finite difference method for Caputo-Fabrizio time-fractional distributed-order diffusion equationA Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential EquationA POD-based reduced-order Crank-Nicolson/fourth-order alternating direction implicit (ADI) finite difference scheme for solving the two-dimensional distributed-order Riesz space-fractional diffusion equationFast iterative solvers and simulation for the space fractional Ginzburg-Landau equationsA new fourth-order energy dissipative difference method for high-dimensional nonlinear fractional generalized wave equationsFast solution methods for Riesz space fractional diffusion equations with non-separable coefficientsNumerical treatment of non-linear fourth-order distributed fractional sub-diffusion equation with time-delayEfficient linear energy dissipative difference schemes for the coupled nonlinear damped space fractional wave equationsHigh-order numerical algorithm and error analysis for the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equationA fast implicit difference scheme for a new class of time distributed-order and space fractional diffusion equations with variable coefficientsApproximation methods for solving fractional equationsAlternating-direction implicit finite difference methods for a new two-dimensional two-sided space-fractional diffusion equationA fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equationsError estimate of second-order finite difference scheme for solving the Riesz space distributed-order diffusion equationOn a second order scheme for space fractional diffusion equations with variable coefficientsNumerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularityA fourth-order conservative difference scheme for the Riesz space-fractional sine-Gordon equations and its fast implementationAn efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg-Landau equationsConvergence of an energy-conserving scheme for nonlinear space fractional Schrödinger equations with wave operatorDiscrete spline methods for solving two point fractional Bagley-Torvik equationA finite difference scheme for semilinear space-fractional diffusion equations with time delaySome high order difference schemes for the space and time fractional Bloch-Torrey equationsSecond-order BDF time approximation for Riesz space-fractional diffusion equationsEfficient semi-implicit compact finite difference scheme for nonlinear Schrödinger equations on unbounded domainA second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equationFast direct solver for CN-ADI-FV scheme to two-dimensional Riesz space-fractional diffusion equationsAn efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficientsAn explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional sine-Gordon equationsA fast preconditioned iterative method for two-dimensional options pricing under fractional differential modelsSplit-step alternating direction implicit difference scheme for the fractional Schrödinger equation in two dimensionsCompact difference scheme for a class of fractional-in-space nonlinear damped wave equations in two space dimensionsFourth order finite difference schemes for time-space fractional sub-diffusion equationsNumerical analysis and fast implementation of a fourth-order difference scheme for two-dimensional space-fractional diffusion equationsA novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equationsStability and convergence of finite difference method for two-sided space-fractional diffusion equationsSecond order compact difference scheme for time fractional sub-diffusion fourth-order neutral delay differential equationsLie point symmetry analysis of the Harry-Dym type equation with Riemann-Liouville fractional derivativePhysical properties preserving numerical simulation of stochastic fractional nonlinear wave equationAn efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equationExponentially fitted methods for solving time fractional nonlinear reaction-diffusion equationAn implicit midpoint difference scheme for the fractional Ginzburg-Landau equationStability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficientsLinear implicit finite difference methods with energy conservation property for space fractional Klein-Gordon-Zakharov systemError estimates of a spectral Petrov-Galerkin method for two-sided fractional reaction-diffusion equationsA general framework for the numerical analysis of high-order finite difference solvers for nonlinear multi-term time-space fractional partial differential equations with time delayAn implicit semi-linear discretization of a bi-fractional Klein-Gordon-Zakharov system which conserves the total energyAn efficient difference scheme for the coupled nonlinear fractional Ginzburg–Landau equations with the fractional LaplacianAn efficient second-order convergent scheme for one-side space fractional diffusion equations with variable coefficientsFast algorithms for high-order numerical methods for space-fractional diffusion equationsA fourth-order scheme for space fractional diffusion equationsAn explicit form for higher order approximations of fractional derivativesA conservative splitting difference scheme for the fractional-in-space Boussinesq equationFinite element method for two-sided fractional differential equations with variable coefficients: Galerkin approachAn effective dissipation-preserving fourth-order difference solver for fractional-in-space nonlinear wave equationsA high-order algorithm for time-Caputo-tempered partial differential equation with Riesz derivatives in two spatial dimensionsTwo energy-preserving numerical models for a multi-fractional extension of the Klein-Gordon-Zakharov systemOn \(\tau\) matrix-based approximate inverse preconditioning technique for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equationsInvestigations on several high-order ADI methods for time-space fractional diffusion equationFast ADI difference/compact difference schemes for the nonlocal evolution equation with weakly singular kernels in three dimensionsAn efficient multigrid method with preconditioned smoother for two-dimensional anisotropic space-fractional diffusion equationsSome numerical extrapolation methods for the fractional sub-diffusion equation and fractional wave equation based on the \(L1\) FormulaTensor-train format solution with preconditioned iterative method for high dimensional time-dependent space-fractional diffusion equations with error analysisA Splitting Preconditioner for Toeplitz-Like Linear Systems Arising from Fractional Diffusion EquationsTime-space spectral Galerkin method for time-fractional fourth-order partial differential equationsA wavelet collocation method based on Gegenbauer scaling function for solving fourth-order time-fractional integro-differential equations with a weakly singular kernelA class of preconditioner for solving the Riesz distributed-order nonlinear space-fractional diffusion equationsNumerical methods for fractional partial differential equationsA fourth-order compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equation


Uses Software


Cites Work


This page was built for publication: A fourth-order approximation of fractional derivatives with its applications