Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution
DOI10.1007/s13540-023-00162-3zbMath1522.65148arXiv2302.02632OpenAlexW4376128438MaRDI QIDQ6073813
Weihua Deng, Jing Sun, Daxin Nie
Publication date: 12 October 2023
Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2302.02632
error analysisLaplace operatorfractional sub-diffusion equationcentral finite difference methodmodified schemeaveraged \(L1\) schemeaveraged second order backward difference scheme
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) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)
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Cites Work
- Stability and convergence of finite difference schemes for a class of time-fractional sub-diffusion equations based on certain superconvergence
- Too much regularity may force too much uniqueness
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- Second-order stable finite difference schemes for the time-fractional diffusion-wave equation
- Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. I
- Singularity analysis and asymptotics of Bernoulli sums
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. II
- An averaged \(L 1\)-type compact difference method for time-fractional mobile/immobile diffusion equations with weakly singular solutions
- Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations
- Fractional diffusion-wave equations: hidden regularity for weak solutions
- Convergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth data
- Finite element approximations for fractional evolution problems
- Finite difference/spectral approximations for the time-fractional diffusion equation
- Two high-order time discretization schemes for subdiffusion problems with nonsmooth data
- An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
- Exponential Convolution Quadrature for Nonlinear Subdiffusion Equations with Nonsmooth Initial Data
- Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
- Time Discretization of a Tempered Fractional Feynman--Kac Equation with Measure Data
- Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
- An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data
- Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
- Self-similarity, renormalization, and phase space nonuniformity of Hamiltonian chaotic dynamics
- Optimal Convergence Rates in Time-Fractional Discretisations: The ${\rm L1}$, $\overline{{\rm L1}}$ and Alikhanov Schemes
- An $L1$ Approximation for a Fractional Reaction-Diffusion Equation, a Second-Order Error Analysis over Time-Graded Meshes
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Subdiffusion with a time-dependent coefficient: Analysis and numerical solution
- The Mathematical Theory of Finite Element Methods
- Adaptive Second-Order Crank--Nicolson Time-Stepping Schemes for Time-Fractional Molecular Beam Epitaxial Growth Models
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