
Energy Stable L2 Schemes for TimeFractional PhaseField Equations
In this article, the energy stability of two highorder L2 schemes for t...
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Parallelintime highorder BDF schemes for diffusion and subdiffusion equations
In this paper, we propose a parallelintime algorithm for approximately...
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A new discrete energy technique for multistep backward difference formulas
The backward differentiation formula (BDF) is a useful family of implici...
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On a seventh order convergent weakly Lstable Newton Cotes formula with application on Burger's equation
In this paper we derive 7^th order convergent integration formula in tim...
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The energy technique for the sixstep BDF method
In combination with the Grenander–Szegö theorem, we observe that a relax...
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An efficient secondorder energy stable BDF scheme for the space fractional CahnHilliard equation
The space fractional CahnHilliard phasefield model is more adequate an...
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Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor
In the context of flow visualization a triple decomposition of the veloc...
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Backward difference formula: The energy technique for subdiffusion equation
Based on the equivalence of Astability and Gstability, the energy technique of the sixstep BDF method for the heat equation has been discussed in [Akrivis, Chen, Yu, Zhou, Math. Comp., Revised]. Unfortunately, this theory is hard to extend the timefractional PDEs. In this work, we consider three types of subdiffusion models, namely singleterm, multiterm and distributed order fractional diffusion equations. We present a novel and concise stability analysis of time stepping schemes generated by kstep backward difference formula (BDFk), for approximately solving the subdiffusion equation. The analysis mainly relies on the energy technique by applying GrenanderSzegö theorem. This kind of argument has been widely used to confirm the stability of various Astable schemes (e.g., k=1,2). However, it is not an easy task for the higherorder BDF methods, due to the loss the Astability. The core object of this paper is to fill in this gap.
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