A Fast Temporal Second Order Difference Scheme for the Fractional Sub-diffusion Equations on One Dimensional Space Unbounded Domain

DOI10.4208/jms.v56n2.23.05OpenAlexW4382774794MaRDI QIDQ6121342

Zhi-zhong Sun, Ren-jun Qi

Publication date: 26 February 2024

Published in: Journal of Mathematical Study (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/jms.v56n2.23.05

zbMATH Keywords

energy methoddifference schemefast algorithmfractional sub-diffusion equationsspace unbounded domainhigh-order local artificial boundary conditions

Mathematics Subject Classification ID

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) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Cites Work

• Unnamed Item
• Unnamed Item
• Local artificial boundary conditions for Schrödinger and heat equations by using high-order azimuth derivatives on circular artificial boundary
• Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain
• A new difference scheme for the time fractional diffusion equation
• A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions
• Convergence of difference scheme for heat equation in unbounded domains using artificial boundary conditions
• Efficient implementation to numerically solve the nonlinear time fractional parabolic problems on unbounded spatial domain
• ``Free-space boundary conditions for the time dependent wave equation
• Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity
• A difference scheme for Burgers equation in an unbounded domain
• The fundamental solutions for the fractional diffusion-wave equation
• High-order local artificial boundary conditions for problems in unbounded domains
• A class of artificial boundary conditions for heat equation in unbounded domains
• Polynomial and nonpolynomial spline methods for fractional sub-diffusion equations
• The numerical computation of the time fractional Schrödinger equation on an unbounded domain
• Solution for a fractional diffusion-wave equation defined in a bounded domain
• Obtaining artificial boundary conditions for fractional sub-diffusion equation on space two-dimensional unbounded domains
• Absorbing boundary conditions for the fractional wave equation
• Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data
• A fast temporal second-order compact ADI difference scheme for the 2D multi-term fractional wave equation
• Artificial boundary conditions for nonlinear time fractional Burgers' equation on unbounded domains
• Finite difference/Hermite-Galerkin spectral method for multi-dimensional time-fractional nonlinear reaction-diffusion equation in unbounded domains
• Direct implementation of high order BGT artificial boundary conditions
• A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
• Finite difference/spectral approximations for the time-fractional diffusion equation
• High-order local non-reflecting boundary conditions: a review
• The finite difference approximation for a class of fractional sub-diffusion equations on a space unbounded domain
• A fully discrete difference scheme for a diffusion-wave system
• Some temporal second order difference schemes for fractional wave equations
• High-Order Local Absorbing Boundary Conditions for Heat Equation in Unbounded Domains
• Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media
• The Approximation of the Exact Boundary Conditions at an Artificial Boundary for Linear Elastic Equations and its Application
• A Padé Approximation Method for Square Roots of Symmetric Positive Definite Matrices
• Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation
• Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space
• Numerical methods for fractional partial differential equations
• Fractional Differential Equations
• High-Order Local Absorbing Boundary Conditions for Fractional Evolution Equations on Unbounded Strips
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme
• Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems
• Efficient Numerical Computation of Time-Fractional Nonlinear Schrödinger Equations in Unbounded Domain
• Fractional differentiation matrices with applications
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• High-Order Local Artificial Boundary Conditions for the Fractional Diffusion Equation on One-Dimensional Unbounded Domain
• Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
• Large-Scale Scientific Computing