Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient [PDF]
, 2018 We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient.
Leobacher, Gunther +1 more
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On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations [PDF]
, 2013 This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations.
Karafyllis, Iasson, Krstic, Miroslav
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Discontinuity Propagation in Delay Differential-Algebraic Equations [PDF]
The Electronic Journal of Linear Algebra, 2018 The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencils, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed.
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Some new integral inequalities with mixed nonlinearities for discontinuous functions
Advances in Difference Equations, 2018 In this paper, we establish some new integral inequalities with mixed nonlinearities for discontinuous functions, which provide a handy tool in deriving the explicit bounds for the solutions of impulsive differential equations and differential-integral ...
Haidong Liu
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Electronic Journal of Qualitative Theory of Differential Equations, 2017 We use upper and lower absolutely continuous functions as subsolutions and supersolutions to discontinuous ordinary differential equations. We present sufficient conditions for the existence of extremal solutions to initial value problems. Due to a new
Krzysztof Topolski
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Periodic Solutions in Slowly Varying Discontinuous Differential Equations: The Generic Case
Mathematics, 2021 We study persistence of periodic solutions of perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular periodic solution.
Flaviano Battelli, Michal Fečkan
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Transonic Shocks In Multidimensional Divergent Nozzles [PDF]
, 2010 We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure.
A.G. Kuz’min +24 more
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Minimizers with discontinuous velocities for the electromagnetic variational method
, 2011 The electromagnetic two-body problem has \emph{neutral differential delay} equations of motion that, for generic boundary data, can have solutions with \emph{discontinuous} derivatives. If one wants to use these neutral differential delay equations with \
A. Bellen +6 more
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Discontinuous hp-Finite Element Methods for Advection-Diffusion Problems [PDF]
, 2000 We consider the hp-version of the discontinuous Galerkin finite element method for second-order partial differential equations with nonnegative characteristic form.
Houston, P. +2 more
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Discontinuous differential equations, II
Journal of Differential Equations, 1979 See the review (Autorreferat) in Zbl 0365.34017.
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