5 papers
TASE-Stabilized Time-Evolving Natural Gradient Methods for Diffusion-Dominated PDEs
Zihao Shi, Dongling Wang
The Time-Evolving Natural Gradient (TENG) method evolves neural approximations of time-dependent partial differential equations by projecting time-discrete target states onto the n…
Average block nonlinear Kaczmarz methods with adaptive momentum for nonlinear systems of equations
Renjie Ding, Dongling Wang, Jun Zou
The Kaczmarz method is widely recognized as an efficient iterative algorithm for solving large-scale linear systems, owing to its simplicity and low memory requirements. However, t…
Preserving Conservation Laws in the Time-Evolving Natural Gradient Method via Relaxation and Projection Techniques
Zihao Shi, Dongling Wang
Neural networks have demonstrated significant potential in solving partial differential equations (PDEs). While global approaches such as Physics-Informed Neural Networks (PINNs) o…
Asymptotic stability of many numerical schemes for phase-field modeling
Pansheng Li, Dongling Wang
In the recent breakthrough work \cite{xu2023lack}, a rigorous numerical analysis was conducted on the numerical solution of a scalar ODE containing a cubic polynomial derived from…
Mittag-Leffler stability of complete monotonicity-preserving schemes for time-dependent coefficients sub-diffusion equations
Wen Dong, Dongling Wang
A key characteristic of the anomalous sub-solution equation is that the solution exhibits algebraic decay rate over long time intervals, which is often refered to the Mittag-Leffle…