On high order numerical schemes for fractional differential equations by block-by-block approach

DOI10.1016/j.amc.2022.127098OpenAlexW4221052734WikidataQ115361058 ScholiaQ115361058MaRDI QIDQ2139817

Xiaoli Chen, Dan Zhao, Mianfu She, Li-Li Li

Publication date: 19 May 2022

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

Full work available at URL: https://doi.org/10.1016/j.amc.2022.127098

zbMATH Keywords

convergencenon-smooth solutionnonlinear fractional differential equationhigh order scheme

Mathematics Subject Classification ID

Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) General theory for ordinary differential equations (34Axx)

Related Items (1)

A block-by-block approach for nonlinear fractional integro-differential equations

Cites Work

• Unnamed Item
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• The spectral analysis for a singular fractional differential equation with a signed measure
• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• A new difference scheme for the time fractional diffusion equation
• Error estimate for the numerical solution of fractional reaction-subdiffusion process based on a meshless method
• Fractional-time Schrödinger equation: fractional dynamics on a comb
• Numerical analysis and physical simulations for the time fractional radial diffusion equation
• Solving a nonlinear fractional differential equation using Chebyshev wavelets
• An approximate method for numerical solution of fractional differential equations
• Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Detailed error analysis for a fractional Adams method
• Recovering a source term in the time-fractional Burgers equation by an energy boundary functional equation
• Long time numerical behaviors of fractional pantograph equations
• An implicit difference scheme for the time-fractional Cahn-Hilliard equations
• Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution
• A novel scheme to capture the initial dramatic evolutions of nonlinear subdiffusion equations
• A transformed \(L 1\) method for solving the multi-term time-fractional diffusion problem
• An efficient spectral-Galerkin method for fractional reaction-diffusion equations in unbounded domains
• A new parallel difference algorithm based on improved alternating segment Crank-Nicolson scheme for time fractional reaction-diffusion equation
• A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg-Landau equations
• An L1 Legendre-Galerkin spectral method with fast algorithm for the two-dimensional nonlinear coupled time fractional Schrödinger equation and its parameter estimation
• Numerical schemes for solving the time-fractional dual-phase-lagging heat conduction model in a double-layered nanoscale thin film
• Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation
• Linearized Galerkin FEMs for nonlinear time fractional parabolic problems with non-smooth solutions in time direction
• Convergence and stability of compact finite difference method for nonlinear time fractional reaction-diffusion equations with delay
• Fractional-order Legendre-collocation method for solving fractional initial value problems
• Linearized Crank-Nicolson scheme for the nonlinear time-space fractional Schrödinger equations
• A high order schema for the numerical solution of the fractional ordinary differential equations
• A fully discrete difference scheme for a diffusion-wave system
• Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems
• Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations
• Implicit-Explicit Difference Schemes for Nonlinear Fractional Differential Equations with Nonsmooth Solutions
• Weakly Singular Discrete Gronwall Inequalities
• Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Time fractional Schrödinger equation
• Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations
• The Finite Difference Methods for Fractional Ordinary Differential Equations
• A Novel Numerical Approach to Time-Fractional Parabolic Equations with Nonsmooth Solutions
• Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems
• Fractional Crank–Nicolson–Galerkin finite element scheme for the time‐fractional nonlinear diffusion equation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Analysis of fractional differential equations
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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