Results 241 to 250 of about 159,062 (288)

Periodic Solutions of Nonlinear Nonautonomous Systems of Ordinary Differential Equations

Differential Equations, 2001
The system of differential equations \[ \dot x = (A(t) + B(t, \lambda) + F(t, x, \lambda))x, \quad \tag{1} \] is considered, where \(x\in E_n, A(t), B(t, \lambda)\) and \(F(t, x, \lambda)\) are \(n \times n\)-matrix functions \(\omega\)-periodic in \(t,\lambda\) is a parameter and \(E_s\) is an \(s\)-dimensional vector space.
Terekhin, M. T., Retyunskikh, N. V.
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Asymptotic decomposition of systems of nonlinear ordinary differential equations

Ukrainian Mathematical Journal, 1984
The construction of solutions of non linear ODE's by meams of asymptotic expansions relies on a relative-magnitude ordering of terms in the ODE's. This is most easily accomplished with the help of a 'small parameter'. Since usual small parameter expansions are not always successful, an alternate construction method is proposed.
Mitropol'skij, Yu. A., Lopatin, A. K.
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On stability of nonlinear systems of ordinary differential equations

Applied Mathematics and Computation, 2000
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El-Sheikh Aly, M. M. A., Soliman, A. A., Abd Alla, M. H.   +2 more
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Systems of ordinary differential equations with nonlinear superposition principles

Physica D: Nonlinear Phenomena, 1982
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Anderson, R. L., Harnad, J., Winternitz, P.   +2 more
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Nonlinear boundary-value problems for systems of ordinary differential equations

Ukrainian Mathematical Journal, 1998
The author studies a boundary value problem for a system of nonlinear ordinary differential equations \[ (1)\quad \dot z=Z(z,t), \qquad (2) \quad lz= \varphi(z(\cdot)), \] where the nonlinear \(n\)-dimensional vector function \(Z(z,t)\) satisfies the conditions: \(Z( \cdot ,t)\in C^{1}[\|z-z_{0}\|\leq q]\) and \(Z(z, \cdot)\in C[a,b];\) \(l\) is a ...
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Parameter sensitivity of systems described by nonlinear ordinary differential equations

AIChE Journal, 1971
AbstractAn approximate analytical method is developed to estimate the parameter sensitivity of the solution of a set of nonlinear ordinary differential equations describing a system which exhibits periodic behavior. An approximate solution is constructed in terms of both the approximate periodic solution determined from Galerkin equations and the ...
R. J. Rayzak, Rein Luus
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On Nonlinear Systems of Ordinary Differential Equations

1988
The paper gives some analytical representations and numerical methods for the solutions of systems of ordinary differential equations with emphasis of the formal side, using the connection to the linear partial differential equations in the case first mentioned.
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Exponential Dichotomy of Nonlinear Systems of Ordinary Differential Equations

1985
Publisher Summary This chapter discusses exponential dichotomy of nonlinear systems of ordinary differential equations. A dichotomy, exponential or ordinary, is a type of conditional stability. A linear differential equation possesses a dichotomy if there exists an invariant splitting or a continuous decomposition of the Euclidean space into stable ...
S. Elaydi, O. Hajek
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Asymptotic Behavior of the Solutions of Nonlinear Systems of Ordinary Differential Equations

Journal of Mathematical Sciences, 2015
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Evtukhov, V. M., Talimonchak, M. A.
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Exploring inductive linearization for pharmacokinetic–pharmacodynamic systems of nonlinear ordinary differential equations

Journal of Pharmacokinetics and Pharmacodynamics, 2017
Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand.
Chihiro Hasegawa, Stephen B. Duffull
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