4 papers · 1 filter
Implicit and implicit--explicit high-order BDF methods for coupled elliptic--parabolic systems
Georgios Akrivis, Minghua Chen, Fan Yu
First-order fully implicit as well as implicit--explicit schemes for coupled elliptic-parabolic systems are discussed in [Ern and Meunier, ESAIM: M2AN, 2009] and [Altmann et al., M…
Correction of weighted and shifted seven-step BDF for parabolic equations with nonsmooth data
Minghua Chen, Jiankang Shi, Fan Yu +1
It is well known that the seven-step backward difference formula (BDF) is unstable for the parabolic equations, since it is not even zero-stable. However, a linear combination of t…
Multiprecision computing for multistage fractional physics-informed neural networks
Na Xue, Minghua Chen
Fractional physics-informed neural networks (fPINNs) have been successfully introduced in [Pang, Lu and Karniadakis, SIAM J. Sci. Comput. 41 (2019) A2603-A2626], which observe rela…
The weighted and shifted seven-step BDF method for parabolic equations
Georgios Akrivis, Minghua Chen, Fan Yu
Stability of the BDF methods of order up to five for parabolic equations can be established by the energy technique via Nevanlinna--Odeh multipliers. The nonexistence of Nevanlinna…