Results 231 to 240 of about 39,621 (275)

The discontinuous Galerkin method for general nonlinear third-order ordinary differential equations

Applied Numerical Mathematics, 2021
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Mahboub Baccouch
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Efficient Ordinary Differential Equation-Based Discontinuous Galerkin Method for Viscoelastic Wave Modeling

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
Qiwei Zhan, Mingwei Zhuang, Qingtao Sun, Qiang Ren, Yi Ren, Yiqian Mao, Qing Huo Liu   +6 more
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Viability theory applied to discontinuous ordinary differential equations

AIP Conference Proceedings, 2009
In this paper we collect some concepts about viability theory that we can use in order to obtain some results for the existence of solutions (and, in many cases, extremal solutions) of discontinuous differential equations. Concretely, we show in this way some results for initial value problems, given in [1], functional value problems, given in [2], and
Rubén Figueroa Sestelo, Rodrigo López Pouso, Alberto Cabada, Eduardo Liz, Juan J. Nieto   +4 more
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The decomposition method for ordinary differential equations with discontinuities

Applied Mathematics and Computation, 2002
In 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.
Casasús, Luis, Al-Hayani, Waleed
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Ordinary differential equations and systems with time-dependent discontinuity sets

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2004
In 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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Efficient integration over discontinuities in ordinary differential equation simulations

Mathematics and Computers in Simulation, 1978
Abstract This paper introduces a new method of detecting and handling discontinuities in arbitrary functions which form part of an ordinary differential equation set. The method has been implemented in conjunction with the Gear[6] integration algorithm for stiff equation sets, published by Hindmarsh[9], but the philosophy applies to any predictor ...
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Approximation of discontinuous solutions of ordinary differential equations by polynomial splines

USSR Computational Mathematics and Mathematical Physics, 1977
Abstract A LINEAR boundary value problem of arbitrary order with a finite number of points of discontinuity at which certain splicing conditions are specified is considered. An approximate solution is sought by the collocation method in the space of splines with multiple nodes at the points of discontinuity.
Vasil'ev, M. G., Juferev, V. S.
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Solving Discontinuous Ordinary Differential Equations

1995
In 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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Efficient automatic integration of ordinary differential equations with discontinuities

Mathematics and Computers in Simulation, 1981
Abstract This paper describes a method of automatically detecting and accurately locating discontinuities which occur in many applications of ordinary differential equations. The integration formula is a Runge-Kutta so chosen that accurate values between integration points can be found by Hermite interpolation.
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Discontinuous ordinary differential equations and stabilization

2017
In 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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