Results 211 to 220 of about 1,675 (248)
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Nonordered discontinuous upper and lower solutions for first-order ordinary differential equations
Nonlinear Analysis: Theory, Methods & Applications, 2001The author studies the first-order equations \[ x'(t)=f(t,x(t)), \text{ for a. e. } t \in I=[0,1], \quad x(0)=x_0, \] and \[ x'(t)=f(t,x(t)), \text{ for a. e. } t \in I=[0,1], \quad x(1)=y_0, \] where \(f:I\times \mathbb{R} \to \mathbb{R}\) is a Carathéodory function.
Rodrigo López-Pouso
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IEEE Transactions on Geoscience and Remote Sensing, 2017
We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave propagation in viscous media. To include the attenuation and dispersion due to the quality factor in time domain, several sets of auxiliary ordinary differential equations (AODEs) are added. Unlike the conventional auxiliary partial differential equation-based
Qing Huo Liu, Yi Ren, Qiwei Zhan
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We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave propagation in viscous media. To include the attenuation and dispersion due to the quality factor in time domain, several sets of auxiliary ordinary differential equations (AODEs) are added. Unlike the conventional auxiliary partial differential equation-based
Qing Huo Liu, Yi Ren, Qiwei Zhan
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On periodic solutions of ordinary differential equations with discontinuous right-hand side
Mathematical Notes, 2006The author studies the existence of vector-valued periodic solutions of differential equations or inclusions of first and second order by a modification of the method of translation along trajectories due to Filippov. Such modification does not require the uniqueness of the solution of the Cauchy problem.
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Discontinuous scalar functions and ordinary differential equations
Mathematical Systems Theory, 1974exaly +3 more sources
The decomposition method for ordinary differential equations with discontinuities
Applied Mathematics and Computation, 2002In this paper, the decomposition method is applied to the Initial Value Problem (IVP) for ordinary differential equations with discontinuities for both linear and nonlinear cases.
Luis Casasús, Waleed Al-Hayani
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On the Neumann Problem for an Ordinary Differential Equation with Discontinuous Right-Hand Side
Differential Equations, 2005The authors consider the following Neumann problem with discontinuous right-hand side \[ x''\in g(t,x,x'),\tag{1} \] \[ x'(0)=r,\;x'(T)=s, \tag{2} \] where \(g:U\rightarrow \mathbb{R}\) is a multifunction, \(U=(a,b)\times \mathbb{R}\times \mathbb{R ...
Zuev, A. V., Filippov, V. V.
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Applied Mathematics and Computation, 2010
The authors consider the following initial value problem for nonlinear ordinary differential equations \[ u'=f(x,u), \quad t\in(0,T], \quad u(0)=u_{0}. \] Let \(\mathcal{T}_{h}:0=t_{0}
Kang Deng, Zhiguang Xiong
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The authors consider the following initial value problem for nonlinear ordinary differential equations \[ u'=f(x,u), \quad t\in(0,T], \quad u(0)=u_{0}. \] Let \(\mathcal{T}_{h}:0=t_{0}
Kang Deng, Zhiguang Xiong
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Ordinary differential equations and systems with time-dependent discontinuity sets
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2004In this paper we prove new existence results for non-autonomous systems of first order ordinary differential equations under weak conditions on the nonlinear part. Discontinuities with respect to the unknown are allowed to occur over general classes of time-dependent sets which are assumed to satisfy a kind of inverse viability condition.
Cid, Ángel J., Pouso, Rodrigo L.
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Discontinuous ordinary differential equations and stabilization
2017In the thesis some techniques of discontinuous differential equations and nonsmooth analysis are developed in order to deal with the stabilization problem of nonlinear systems.
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Solving Discontinuous Ordinary Differential Equations
1995In this paper we generalize the basic notations of the Liouville-Ritt-Risch theory of closed-form solutions to discontinuous field extensions. Our aim is to extend the theory of differential fields such that the “classical algorithm” like the Risch structure theorem and the algorithm solving the Risch differential equation can be extended to handle ...
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