scholarly journals Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and SomeError Analysis

2022 ◽  
Vol 130 (1) ◽  
pp. 299-313 ◽  
Author(s):  
Radwan Abu-Gdairi ◽  
Shatha Hasan ◽  
Shrideh Al-Omari ◽  
Mohammad Al-Smadi ◽  
Shaher Momani
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Reproducing Kernel ◽  
Differential Systems ◽  
Kernel Approach

A Block Implicit Advanced Step-point (BIAS) Algorithm for Stiff Differential Systems

2006 ◽  
Vol 2 (1-2) ◽  
pp. 51-58 ◽  
Author(s):  
G. Psihoyios
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Detailed Account ◽  
Differential Systems ◽  
Stiff Ordinary Differential Equations ◽  
New Methods ◽  
Future Paper ◽  
Near Future

In this paper we propose a new block implicit multistep algorithm, which has been constructed with the aim to successfully tackle the numerical solution of stiff ordinary differential equations. In order to maximise the chances of producing a good new scheme, the first mandatory step is to ensure it incorporates very good theoretical properties. A rather detailed account of the new methods is presented and the properties of the algorithm will be discussed in some detail. In the near future we will also have the opportunity to evaluate the implementation potential of the scheme in a future paper.

scholarly journals Chaos in an anharmonic oscillator

1995 ◽  
Vol 37 (2) ◽  
pp. 186-207 ◽  
Author(s):  
J. R. Christie ◽  
K. Gopalsamy
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous System ◽  
Anharmonic Oscillator ◽  
Homoclinic Orbits ◽  
Chaotic Behaviour ◽  
Differential Systems ◽  
Melnikov's Method ◽  
One Dimensional ◽  
Melnikov’S Method

AbstractUsing Melnikov's method, the existence of chaotic behaviour in the sense of Smale in a particular time-periodically perturbed planar autonomous system of ordinary differential equations is established. Examples of planar autonomous differential systems with homoclinic orbits are provided, and an application to the dynamics of a one-dimensional anharmonic oscillator is given.

scholarly journals Algebraic Criteria of the Integral Separation for Solving Certain Classes of Ordinary Differential Equations Systems

2020 ◽  
pp. 1-14
Author(s):  
A. A. Akhrem ◽  
A. P. Nosov
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Qualitative Theory ◽  
Small Perturbations ◽  
Differential Systems ◽  
Fundamental Properties ◽  
Linear Differential Systems ◽  
Integral Separation ◽  
Linear Differential

One of the important directions of the qualitative theory of ordinary differential equations is to study the properties of linear systems that satisfy the condition of integral separation. Anyway, integral separation becomes apparent in all studies concerning the asymptotic behavior of the solutions for the linear systems under the action of small perturbations.The papers of V.M. Millionschikov, B.F. Bylov, N.A. Izobov, I.N. Sergeev et al. proved that the available integral separation is the main reason for the rough stability of the characteristic Lyapunov exponents, the rough stability of the highest Lyapunov exponent, and the rough diagonalizability of systems by Lyapunov transformations, and other fundamental properties of linear differential systems.The paper presents the basic properties of the set of linear systems with constant, periodic, reducible coefficients and proves the algebraic criteria for their property of integral separation of solutions to be available.The results can be used in modeling dynamic processes.

Multiplicity and bifurcation of periodic solutions in ordinary differential equations

1979 ◽  
Vol 82 (3-4) ◽  
pp. 225-232 ◽  
Author(s):  
B. Laloux
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Diagonal Matrix ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Linear Differential

SynopsisOne considers the linear differential systems where is a (not necessarily diagonal) matrix and one relates the computation of a general multiplicity defined from this system to the corresponding multiplicity of some eigenvalues of . Then applying these conclusions, one gives simple conditions ensuring the existence of odd or even periodic solutions for systems having the form .

Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 711-724
Author(s):  
Ivan Kiguradze
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Global Asymptotic Stability ◽  
Trivial Solution ◽  
Well Posedness ◽  
Bounded Solutions ◽  
Differential Systems ◽  
Nonlinear Differential Systems

Abstract For systems of nonlinear nonautonomous ordinary differential equations, the conditions, optimal in a certain sense, are established, which guarantee the solvability and well-posedness of the problem on bounded solutions, the vanishing at infinity of all bounded solutions and the global asymptotic stability of a trivial solution.

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