most citedA Structure-Preserving Framework for Solving Parabolic Partial Differential Equations with Neural Networks

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math.NA2023★ 1 cited

A linear doubly stabilized Crank-Nicolson scheme for the Allen-Cahn equation with a general mobility

Dianming Hou, Zhonghua Qiao, Lili Ju

In this paper, a linear second order numerical scheme is developed and investigated for the Allen-Cahn equation with a general positive mobility. In particular, our fully discrete…

math.NA2023

Energy-dissipative spectral renormalization exponential integrator method for gradient flow problems

Dianming Hou, Lili Ju, Zhonghua Qiao

In this paper, we present a novel spectral renormalization exponential integrator method for solving gradient flow problems. Our method is specifically designed to simultaneously s…