On the solutions of a second order nonlinear system with almost periodic forcing

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2009.12.002 ◽

2010 ◽

Vol 15 (11) ◽

pp. 3525-3535 ◽

Author(s):

Muren Lin ◽

Yong-Hui Xia

Keyword(s):

Nonlinear System ◽

Second Order ◽

Almost Periodic ◽

Periodic Forcing

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Corrigendum to “On the solutions of a second order nonlinear system with almost periodic forcing” [Commun Nonlinear Sci Numer Simulat 15 (2010) 3525–3535]

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2010.07.019 ◽

2011 ◽

Vol 16 (3) ◽

pp. 1702

Author(s):

Muren Lin ◽

Yong-Hui Xia

Keyword(s):

Nonlinear System ◽

Second Order ◽

Almost Periodic ◽

Periodic Forcing

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Almost periodic solutions of second order nonlinear differential equations with almost periodic forcing

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1959-0104872-6 ◽

1959 ◽

Vol 10 (3) ◽

pp. 425-425 ◽

Author(s):

C. E. Langenhop ◽

G. Seifert

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Nonlinear Differential Equations ◽

Second Order ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Periodic Forcing

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Dynamics of Second Order Lattice Systems with Almost Periodic Nonlinear Part

Qualitative Theory of Dynamical Systems ◽

10.1007/s12346-021-00497-3 ◽

2021 ◽

Vol 20 (2) ◽

Author(s):

Ahmed Y. Abdallah

Keyword(s):

Second Order ◽

Almost Periodic ◽

Lattice Systems ◽

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Second order linear differential equations with almost periodic solutions

Acta Mathematica Sinica English Series ◽

10.1007/bf02594892 ◽

1991 ◽

Vol 7 (4) ◽

pp. 354-359 ◽

Author(s):

Xiao Tijun ◽

Liang Jin

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Second Order ◽

Linear Differential Equations ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Order Linear ◽

Linear Differential

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Solution of a boundary value problem for a nonlinear system of second order ordinary differential equations

Ukrainian Mathematical Journal ◽

10.1007/bf01085333 ◽

1969 ◽

Vol 20 (1) ◽

pp. 30-39 ◽

Author(s):

Yu. I. Kovach ◽

L. I. Savchenko

Keyword(s):

Nonlinear System ◽

Differential Equations ◽

Boundary Value Problem ◽

Ordinary Differential Equations ◽

Boundary Value ◽

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On the existence of almost periodic solutions of some dissipative second order differential equations

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/bf02418235 ◽

1964 ◽

Vol 65 (1) ◽

pp. 389-405 ◽

Author(s):

J. O. C. Ezeilo

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Second Order ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Second Order Differential Equations

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On energy-optimal controls for a second-order nonlinear system

Radiophysics and Quantum Electronics ◽

10.1007/bf01031082 ◽

1969 ◽

Vol 12 (7) ◽

pp. 835-838

Author(s):

V. P. Savel'ev

Keyword(s):

Nonlinear System ◽

Second Order ◽

Optimal Controls

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Almost periodic solutions of second order systems

Applicable Analysis ◽

10.1080/00036819608840516 ◽

1996 ◽

Vol 63 (3-4) ◽

pp. 389-395

Author(s):

Ahmad Shair ◽

Tineo Antonio

Keyword(s):

Periodic Solutions ◽

Second Order ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Second Order Systems

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Asymptotic behavior and periodic forcing in time for the solutions of a nonlinear system representing a phase change with dissipation

World Congress of Nonlinear Analysts '92 ◽

10.1515/9783110883237.2281 ◽

1996 ◽

pp. 2281-2288

Keyword(s):

Asymptotic Behavior ◽

Nonlinear System ◽

Phase Change ◽

Periodic Forcing

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A High-Order Numerical Method for a Nonlinear System of Second-Order Boundary Value Problems

Mathematical Problems in Engineering ◽

10.1155/2020/6280372 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Minqiang Xu ◽

Jing Niu ◽

Li Guo

Keyword(s):

Nonlinear System ◽

Boundary Value Problems ◽

Numerical Experiments ◽

Reproducing Kernel ◽

Kernel Method ◽

Boundary Value ◽

Linear Equations ◽

Second Order ◽

Reproducing Kernel Method

This paper is concerned with a high-order numerical scheme for nonlinear systems of second-order boundary value problems (BVPs). First, by utilizing quasi-Newton’s method (QNM), the nonlinear system can be transformed into linear ones. Based on the standard Lobatto orthogonal polynomials, we introduce a high-order Lobatto reproducing kernel method (LRKM) to solve these linear equations. Numerical experiments are performed to investigate the reliability and efficiency of the presented method.

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