Continuous-Stage ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions

Mapping Intimacies ◽

10.1007/978-981-16-0147-7_2 ◽

2021 ◽

pp. 47-74

Author(s):

Xinyuan Wu ◽

Bin Wang

Keyword(s):

Second Order ◽

Oscillatory Solutions ◽

Highly Oscillatory ◽

Erkn Integrators

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Stability and Convergence Analysis of ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions

10.1007/978-981-16-0147-7_3 ◽

2021 ◽

pp. 75-122

Author(s):

Xinyuan Wu ◽

Bin Wang

Keyword(s):

Convergence Analysis ◽

Second Order ◽

Stability And Convergence ◽

Oscillatory Solutions ◽

Stability And Convergence Analysis ◽

Highly Oscillatory ◽

Erkn Integrators

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Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.02.020 ◽

2020 ◽

Vol 153 ◽

pp. 352-380 ◽

Author(s):

Changying Liu ◽

Xinyuan Wu

Keyword(s):

Nonlinear Stability ◽

Wave Equations ◽

Second Order ◽

Stability And Convergence ◽

Linear Wave ◽

Highly Oscillatory ◽

Linear Wave Equations ◽

Erkn Integrators

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Energy-preserving exponential integrators of arbitrarily high order for conservative or dissipative systems with highly oscillatory solutions

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110429 ◽

2021 ◽

pp. 110429

Author(s):

Lijie Mei ◽

Li Huang ◽

Xinyuan Wu

Keyword(s):

Dissipative Systems ◽

Oscillatory Solutions ◽

Exponential Integrators ◽

Highly Oscillatory

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A novel class of explicit two-step Birkhoff-Hermite integrators for highly oscillatory second-order differential equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2021.2008916 ◽

2021 ◽

pp. 1-0

Author(s):

Xianfa Hu ◽

Xiong You ◽

Xiong You

Keyword(s):

Differential Equations ◽

Second Order ◽

Second Order Differential Equations ◽

Highly Oscillatory

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Asymptotic-numerical solvers for highly oscillatory second-order differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.11.004 ◽

2019 ◽

Vol 137 ◽

pp. 184-202

Author(s):

Zhongli Liu ◽

Tianhai Tian ◽

Hongjiong Tian

Keyword(s):

Differential Equations ◽

Second Order ◽

Second Order Differential Equations ◽

Highly Oscillatory

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Oscillation-Preserving Integrators for Highly Oscillatory Systems of Second-Order ODEs

10.1007/978-981-16-0147-7_1 ◽

2021 ◽

pp. 1-45

Author(s):

Xinyuan Wu ◽

Bin Wang

Keyword(s):

Second Order ◽

Oscillatory Systems ◽

Highly Oscillatory ◽

Highly Oscillatory Systems

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Existence of Oscillatory Solutions of Second Order Functional Equations with Damping Terms

International Conference on Information Technology and Computer Science, 3rd (ITCS 2011) ◽

10.1115/1.859742.paper115 ◽

2011 ◽

pp. 461-464

Keyword(s):

Functional Equations ◽

Second Order ◽

Oscillatory Solutions

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Classification and Existence of Non-Oscillatory Solutions of Second-Order Neutral Delay Difference Equations

Zeitschrift für Analysis und ihre Anwendungen ◽

10.4171/zaa/1013 ◽

2001 ◽

Vol 20 (1) ◽

pp. 223-234 ◽

Author(s):

Yong Zhou ◽

Binggen Zhang

Keyword(s):

Difference Equations ◽

Second Order ◽

Neutral Delay ◽

Oscillatory Solutions ◽

Delay Difference Equations ◽

Delay Difference

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Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

Abstract and Applied Analysis ◽

10.1155/2012/253107 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18 ◽

Author(s):

M. Tamer Şenel

Keyword(s):

Dynamic Equation ◽

Nonlinear Dynamic ◽

Sufficient Conditions ◽

Second Order ◽

Oscillatory Solutions ◽

Oscillation Criteria ◽

Nonlinear Dynamic Equation ◽

Nonlinear Dynamic Equations ◽

Generalized Riccati Transformation ◽

Type Oscillation

The oscillation of solutions of the second-order nonlinear dynamic equation(r(t)(xΔ(t))γ)Δ+p(t)(xΔ(t))γ+f(t,x(g(t)))=0, with damping on an arbitrary time scaleT, is investigated. The generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for oscillatory solutions of this equation are obtained.

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ASYMPTOTIC EXPANSION AND CONVERGENCE THEOREM OF CONTROL AND OBSERVATION ON THE BOUNDARY FOR SECOND-ORDER ELLIPTIC EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202504003295 ◽

2004 ◽

Vol 14 (03) ◽

pp. 417-437 ◽

Author(s):

LI-QUN CAO

Keyword(s):

Asymptotic Expansion ◽

Elliptic Equation ◽

Asymptotic Expansions ◽

Convergence Theorem ◽

Second Order ◽

Order Elliptic Equation ◽

Oscillating Coefficients ◽

Highly Oscillatory ◽

Second Order Elliptic Equation ◽

The Neumann Problem

In this paper, we shall study systems governed by the Neumann problem of second-order elliptic equation with rapidly oscillating coefficients and with control and observations on the boundary. The multiscale asymptotic expansions of the solution for considering problem in the case without any constraints, and homogenized equation in the case with constraints will be given, their rigorous proofs will also be proposed.

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