Super Exponentially Convergent Approximation to the Solution of the Schrödinger Equation in Abstract Setting

AbstractWe have developed an approximation to the solution of the Schrödinger equation in abstract setting. The accuracy of our approximation depends on the smoothness of this solution. We show that for the analytical initial vectors our approximation possesses a super exponential convergence rate.

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Estimate of exponential convergence rate in total variation by spectral gap

Acta Mathematica Sinica English Series ◽

10.1007/bf02563878 ◽

1998 ◽

Vol 14 (1) ◽

pp. 9-16 ◽

Cited By ~ 5

Author(s):

Chen Mufa

Keyword(s):

Convergence Rate ◽

Total Variation ◽

Spectral Gap ◽

Exponential Convergence ◽

Exponential Convergence Rate

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Estimate the exponential convergence rate of f-ergodicity via spectral gap

Statistics & Probability Letters ◽

10.1016/j.spl.2020.108924 ◽

2021 ◽

Vol 168 ◽

pp. 108924

Author(s):

Xianping Guo ◽

Zhong-Wei Liao

Keyword(s):

Convergence Rate ◽

Spectral Gap ◽

Exponential Convergence ◽

Exponential Convergence Rate

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Estimation of attraction domain and exponential convergence rate of dynamic feedback neural nets

WCC 2000 - ICSP 2000. 2000 5th International Conference on Signal Processing Proceedings. 16th World Computer Congress 2000 ◽

10.1109/icosp.2000.893406 ◽

2002 ◽

Cited By ~ 1

Author(s):

Dongming Zhou ◽

Jianrong Shen ◽

Xiang Ren

Keyword(s):

Convergence Rate ◽

Exponential Convergence ◽

Neural Nets ◽

Attraction Domain ◽

Dynamic Feedback ◽

Exponential Convergence Rate

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Exponential convergence rate estimation for uncertain delayed neural networks of neutral type

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2007.10.043 ◽

2009 ◽

Vol 40 (5) ◽

pp. 2491-2499 ◽

Cited By ~ 16

Author(s):

Chang-Hua Lien ◽

Ker-Wei Yu ◽

Yen-Feng Lin ◽

Yeong-Jay Chung ◽

Long-Yeu Chung

Keyword(s):

Neural Networks ◽

Convergence Rate ◽

Exponential Convergence ◽

Neutral Type ◽

Delayed Neural Networks ◽

Rate Estimation ◽

Exponential Convergence Rate

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Estimation of attraction domain and exponential convergence rate of Hopfield-type associative memory neural network

Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527) ◽

10.1109/wcica.2002.1021529 ◽

2003 ◽

Author(s):

Guanghui Cai ◽

Jihong Shi

Keyword(s):

Neural Network ◽

Convergence Rate ◽

Associative Memory ◽

Exponential Convergence ◽

Attraction Domain ◽

Exponential Convergence Rate

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The Inviscid Limit of the Fractional Complex Ginzburg–Landau Equation

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2016-0017 ◽

2016 ◽

Vol 17 (6) ◽

pp. 333-341

Author(s):

Lijun Wang ◽

Jingna Li ◽

Li Xia

Keyword(s):

Initial Data ◽

Schrödinger Equation ◽

Convergence Rate ◽

Schrodinger Equation ◽

Landau Equation ◽

Limit Behavior ◽

Inviscid Limit ◽

Ginzburg Landau ◽

Ginzburg Landau Equation

AbstractIn this paper, the inviscid limit behavior of solution of the fractional complex Ginzburg–Landau (FCGL) equation$${\partial _t}u + (a + i\nu){\Lambda ^{2\alpha}}u + (b + i\mu){\left| u \right|^{2\sigma}}u = 0, \quad (x, t) \in {{\Cal T}^n} \times (0, \infty)$$is considered. It is shown that the solution of the FCGL equation converges to the solution of nonlinear fractional complex Schrödinger equation, while the initial data${u_0}$is taken in${L^2}, $${H^\alpha}$, and${L^{2\sigma + 2}}$as$a,\, b$tends to zero, and the convergence rate is also obtained.

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