Unconditionally stable and convergent difference scheme for superdiffusion with extrapolation
DOI10.1007/s10915-023-02395-zzbMath1530.65097OpenAlexW4388945222MaRDI QIDQ6184276
Amiya K. Pani, Yubin Yan, Charles Wing Ho Green, Jinping Yang
Publication date: 5 January 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-023-02395-z
stabilityerror estimatesasymptotic expansionextrapolationhigher-order schemetime-fractional wave equation
Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) 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) Extrapolation to the limit, deferred corrections (65B05) Numerical interpolation (65D05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite difference methods for boundary value problems involving PDEs (65N06) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Alternating direction implicit Galerkin finite element method for the two-dimensional fractional diffusion-wave equation
- Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
- Second-order approximations for variable order fractional derivatives: algorithms and applications
- Time-stepping error bounds for fractional diffusion problems with non-smooth initial data
- Higher order numerical methods for solving fractional differential equations
- A compact difference scheme for the fractional diffusion-wave equation
- An ADI Crank-Nicolson orthogonal spline collocation method for the two-dimensional fractional diffusion-wave equation
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- An algorithm for the numerical solution of differential equations of fractional order
- Numerical solution of fractional order differential equations by extrapolation
- Numerical solution of fractional diffusion-wave equation based on fractional multistep method
- Detailed error analysis for a fractional Adams method with graded meshes
- High-order numerical methods for solving time fractional partial differential equations
- The temporal second order difference schemes based on the interpolation approximation for the time multi-term fractional wave equation
- Two alternating direction implicit difference schemes for solving the two-dimensional time distributed-order wave equations
- Some numerical extrapolation methods for the fractional sub-diffusion equation and fractional wave equation based on the \(L1\) Formula
- An H2N2 interpolation for Caputo derivative with order in \((1,2)\) and its application to time-fractional wave equations in more than one space dimension
- Finite difference methods for Caputo-Hadamard fractional differential equations
- A first-order explicit-implicit splitting method for a convection-diffusion problem
- Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity
- A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation
- A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation
- Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes
- A fully discrete difference scheme for a diffusion-wave system
- Numerical Solution of Fractional Diffusion-Wave Equation
- A Second Order Approximation for the Caputo Fractional Derivative
- Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
- Generalized compound quadrature formulae for finite-part integrals
- Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
- On Caputo–Hadamard fractional differential equations
- An extrapolated finite difference method for two-dimensional fractional boundary value problems with non-smooth solution
- High‐order ADI orthogonal spline collocation method for a new 2D fractional integro‐differential problem
- Theory and Numerical Approximations of Fractional Integrals and Derivatives
- Fractional differentiation matrices with applications
- An asymptotic analysis of two algorithms for certain Hadamard finite-part integrals
