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Article
A Unified \(L^2\) Norm Error Analysis of SAV-BDF Schemes for the Incompressible Navier–Stokes Equations
This article is concerned with the \(L^2\) L 2 ...
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Article
Asymptotically Compatible Energy and Dissipation Law of the Nonuniform L2- \(1_{\sigma }\) Scheme for Time Fractional Allen–Cahn Model
We build an asymptotically compatible energy of the variable-step L2- \(1_{\sigma }\) 1
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Article
A multi-physical structure-preserving method and its analysis for the conservative Allen-Cahn equation with nonlocal constraint
The conservative Allen-Cahn equation satisfies three important physical properties, namely the mass conservation law, the energy dissipation law, and the maximum bound principle. However, very few numerical me...
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Article
Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators
The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-step** schemes for nonlocal operators. In this work, we present a novel an...
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Article
Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations
This work is concerned with numerical analysis of the variable-step time filtered backward Euler scheme (see e.g. DeCaria in SIAM J Sci Comput 43(3):A2130–A2160, 2021) for linear parabolic equations. To this e...
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Article
Mesh-Robustness of an Energy Stable BDF2 Scheme with Variable Steps for the Cahn–Hilliard Model
The two-step backward differential formula (BDF2) with unequal time-steps is applied to construct an energy stable convex-splitting scheme for the Cahn–Hilliard model. We focus on the numerical influences of t...
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Article
Energy Stability of BDF Methods up to Fifth-Order for the Molecular Beam Epitaxial Model Without Slope Selection
The backward differential formulas of order \(\mathrm {k}\) k (BDF- ...
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Article
Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
In this work, we are concerned with the stability and convergence analysis of the second-order backward difference formula (BDF2) with variable steps for the molecular beam epitaxial model without slope select...
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Article
A second-order fast compact scheme with unequal time-steps for subdiffusion problems
In consideration of the initial singularity of the solution, a temporally second-order fast compact difference scheme with unequal time-steps is presented and analyzed for simulating the subdiffusion problems ...
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Article
Superconvergence Error Estimate of a Finite Element Method on Nonuniform Time Meshes for Reaction–Subdiffusion Equations
In this paper, we consider superconvergence error estimates of finite element method approximation of Caputo’s time fractional reaction–subdiffusion equations under nonuniform time meshes. For the standard Gal...
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Article
Simple maximum principle preserving time-step** methods for time-fractional Allen-Cahn equation
Two fast L1 time-step** methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional Allen-Cahn equation with Caputo’s derivative. The time mesh is refine...
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Article
Sharp H1-norm error estimate of a cosine pseudo-spectral scheme for 2D reaction-subdiffusion equations
A finite difference cosine pseudo-spectral scheme is presented for solving a linear reaction-subdiffusion problem with Neumann boundary conditions. The nonuniform version of L1 formula is employed for approxim...
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Article
Unconditional Convergence of a Fast Two-Level Linearized Algorithm for Semilinear Subdiffusion Equations
A fast two-level linearized scheme with nonuniform time-steps is constructed and analyzed for an initial-boundary-value problem of semilinear subdiffusion equations. The two-level fast L1 formula of the Caputo...
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Article
Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations
Two fully discrete methods are investigated for simulating the distributed-order sub-diffusion equation in Caputo’s form. The fractional Caputo derivative is approximated by the Caputo’s BDF1 (called L1 early)...
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Article
A Weighted ADI Scheme for Subdiffusion Equations
A weighted ADI scheme is proposed for solving two-dimensional anomalous diffusion equations with the fractional Caputo derivative. The Alikhanov formula (J Comput Phys 280:424–438, 2015) with a weaker assumption ...
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Article
Stability and Convergence of Modified Du Fort–Frankel Schemes for Solving Time-Fractional Subdiffusion Equations
A class of modified Du Fort–Frankel-type schemes is investigated for fractional subdiffusion equations in the Jumarie’s modified Riemann–Liouville form with constant, variable or distributed fractional order. ...
