A Liouville’s Formula for Systems with Reflection

In this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems of ODEs (ordinary differential equations) with reflection. We also present a conjecture for the general case and an application to coupled harmonic oscillators.

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Optimal Estimation of Unknown Right-Hand Sides of First Order Linear Systems of Periodic Ordinary Differential Equations from Indirect Noisy Observations of Their Solutions

2020 IEEE 2nd International Conference on System Analysis & Intelligent Computing (SAIC) ◽

10.1109/saic51296.2020.9239223 ◽

2020 ◽

Author(s):

Oleksandr Nakonechnyi ◽

Yuri Podlipenko

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Linear Systems ◽

Optimal Estimation ◽

Order Linear ◽

First Order ◽

Right Hand

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On the solvability of the modified Cauchy problem for linear systems of generalized ordinary differential equations with singularities

Georgian Mathematical Journal ◽

10.1515/gmj-2020-2052 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Malkhaz Ashordia ◽

Inga Gabisonia ◽

Mzia Talakhadze

Keyword(s):

Cauchy Problem ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Linear Systems ◽

Unique Solvability ◽

Sufficient Conditions ◽

The Cauchy Problem ◽

Generalized Ordinary Differential Equations

AbstractEffective sufficient conditions are given for the unique solvability of the Cauchy problem for linear systems of generalized ordinary differential equations with singularities.

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On numerical isolation of the solutions tending to zero at infinity of certain two-dimensional non-linear sets of ordinary differential equations

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(70)90072-8 ◽

1970 ◽

Vol 10 (1) ◽

pp. 95-111

Author(s):

N.B. Konyukhova

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Two Dimensional ◽

Linear Sets ◽

Non Linear

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Asymptotic Behavior of Solutions of Linear Systems of Ordinary Differential Equations Near an Irregular Singular Point

American Journal of Mathematics ◽

10.2307/2373271 ◽

1969 ◽

Vol 91 (1) ◽

pp. 95 ◽

Cited By ~ 6

Author(s):

Donald A. Lutz

Keyword(s):

Asymptotic Behavior ◽

Singular Point ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Linear Systems ◽

Asymptotic Behavior Of Solutions ◽

Irregular Singular Point

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Application of Homotopy Perturbation Method to Solve Linear and Non-Linear Systems of Ordinary Differential Equations and Differential Equation of Order Three

Journal of Applied Sciences ◽

10.3923/jas.2008.1256.1261 ◽

2008 ◽

Vol 8 (7) ◽

pp. 1256-1261 ◽

Cited By ~ 11

Author(s):

D.D. Ganji . ◽

H. Mirgolbabaei . ◽

Me. Miansari . ◽

Mo. Miansari .

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Perturbation Method ◽

Ordinary Differential Equations ◽

Linear Systems ◽

Homotopy Perturbation Method ◽

Homotopy Perturbation ◽

Non Linear ◽

Non Linear Systems

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Some Invariant Solutions of Two-Dimensional Elastodynamics in Linear Homogeneous Isotropic Materials

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.12-m1257 ◽

2013 ◽

Vol 5 (2) ◽

pp. 212-221

Author(s):

Houguo Li ◽

Kefu Huang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Theoretical Method ◽

Two Dimensional ◽

Invariant Solutions ◽

Partial Differential ◽

Isotropic Materials ◽

Group Theoretical Method ◽

Infinitesimal Operators

AbstractInvariant solutions of two-dimensional elastodynamics in linear homogeneous isotropic materials are considered via the group theoretical method. The second order partial differential equations of elastodynamics are reduced to ordinary differential equations under the infinitesimal operators. Three invariant solutions are constructed. Their graphical figures are presented and physical meanings are elucidated in some cases.

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