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math.NA2020★ 2 cited
Deep Domain Decomposition Method: Elliptic Problems
Wuyang Li, Xueshuang Xiang, Yingxiang Xu
This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decompos…
math.NA2012★ 3 cited
Numerical Computation of Takens-Bogdanov Points for Delay Differential Equations
Yingxiang Xu, Vital D. Mabonzo
The paper presents a numerical technique for computing directly the Takens-Bogdanov points in the nonlinear system of differential equations with one constant delay and two paramet…
math.NA2012
Preservation of Takens-Bogdanov bifurcations for delay differential equations by Euler discretization
Yingxiang Xu, Chengchun Gong
A new technique for calculating the normal forms associated with the map restricted to the center manifold of a class of parameterized maps near the fixed point is given first. The…