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…
A Second-order method on graded meshes for fractional Laplacian via Riesz fractional derivative with a singular source term
Minghua Chen, Jianxing Han, Jiankang Shi +1
The high-order numerical analysis for fractional Laplacian via the Riesz fractional derivative, under the low regularity solution, has presented significant challenges in the past…
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…