Model Reduction for Second Order in Time Nonlinear Dissipative Autonomous Dynamic Systems

2017 ◽  
Vol 1 (1) ◽  
pp. 53-63
Author(s):  
Yan Liu ◽  
Jiazhong Zhang ◽  
Jiahui Chen ◽  
Yamiao Zhang
Keyword(s):  
Model Reduction ◽  
Dynamic Systems ◽  
Second Order ◽  
Second Order In Time

scholarly journals H2 model reduction for diffusively coupled second-order networks by convex-optimization

Automatica ◽  
2022 ◽  
Vol 137 ◽  
pp. 110118
Author(s):  
Lanlin Yu ◽  
Xiaodong Cheng ◽  
Jacquelien M.A. Scherpen ◽  
Junlin Xiong
Keyword(s):  
Convex Optimization ◽  
Model Reduction ◽  
Second Order

scholarly journals An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Lei Ren ◽  
Lei Liu
Keyword(s):  
Finite Difference ◽  
Fourth Order ◽  
Difference Method ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Approximation Formula ◽  
Discrete Energy ◽  
Compact Finite Difference ◽  
Second Order In Time

In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain 2-α in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the L2-1σ approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results.

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