Numerical Solution of the Coupled System of Nonlinear Fractional Ordinary Differential Equations
Advances in Applied Mathematics and Mechanics, 2017AbstractIn this paper, we consider the numerical method that is proposed and analyzed in [J. Cao and C. Xu, J. Comput. Phys., 238 (2013), pp. 154–168] for the fractional ordinary differential equations. It is based on the so-called block-by-block approach, which is a common method for the integral equations.
Zhou, Xiaojun, Xu, Chuanju
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Periodic Solutions of a Class of Nonlinear Systems of Ordinary Differential Equations
Differential Equations, 2004The existence of periodic solutions of second-order differential equations has been studied permanently in the 20th century. In particular, in the last ten years, some studies were concentrated on the existence of multiple periodic solutions. The paper is also in this direction. It is based on using Lagrange multipliers in combination with the fibering
Marino, G., Toskano, R.
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Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations
AIP Conference Proceedings, 2015In this paper, Bernstein polynomials method (B-polynomials) is applied to solve nonlinear stiff systems of ordinary differential equations. We present an approximate solution that depends on Bernstein polynomials method and collocation points. The procedure of the method will be explained briefly and illustrative examples are included to demonstrate ...
Mohammed ALshbool, Ishak Hashim
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Chaotic attractors in nonlinear dissipative systems of ordinary differential equations
Computational Mathematics and Modeling, 2008The goal of this article is to establish the nature, the processes of birth, and the principles of creation of attractors of three-dimensional nonlinear autonomous dissipative systems of ordinary differential equations (ODE) with singular cycles.
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Analytic solution for a nonlinear chemistry system of ordinary differential equations
Nonlinear Dynamics, 2011In this paper, under investigation is a nonlinear chemistry system of ordinary differential equations, whose mechanism is exemplified by certain radioactive series, hydrolyses, and reaction of potassium permanganate, oxalic, and manganous sulfate. Via symbolic computation, an analytic solution for the system is obtained, which has higher accuracy and ...
Li-Cai Liu +4 more
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Robust Model Predictive Control With Neural Ordinary Differential Equations for Nonlinear Systems
Optimal Control Applications and MethodsABSTRACTThis article presents a model predictive control (MPC) strategy that leverages neural ordinary differential equations (NODEs) to address the persistent issue of model mismatch in nonlinear systems. A residual model based on NODEs is employed to capture the differences between the actual system dynamics and conventional models.
Xuyu Shen +4 more
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Neural ordinary differential gray algorithm to forecasting nonlinear systems
Advances in Engineering Software, 2022ZY Chen +3 more
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Existence of Small Periodic Solutions of Nonlinear Systems of Ordinary Differential Equations
Ukrainian Mathematical Journal, 2001The author deals with the system \[ \dot x=A(t,\lambda)x+F(t,x,\lambda)x,\tag{1} \] with \(\dim x=n\), \(A(t,\lambda)\) and \(F(t,x,\lambda)\) \(n\times n\)-matrix-valued \(\omega \)-periodic functions in \(t\) and \(\lambda \) an \(r\)-dimensional parameter.
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Nonlinear System Identification for Quadrotors with Neural Ordinary Differential Equations
2023 IEEE International Conference on Unmanned Systems (ICUS), 2023Mingqian Wang +7 more
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On the asymptotic behaviour of nonlinear systems of ordinary differential equations
Glasgow Mathematical Journal, 1985In this paper we study the asymptotic behaviour of the following systems of ordinary differential equations:where the identically zero function is a solution of (N) i.e. f(t, 0)=0 for all time t. Suppose one knows that all the solutions of (N) which start near zero remain near zero for all future time or even that they approach zero as time increases ...
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