Results 1 to 10 of about 26,290 (93)
A Survey on Continuous Time Computations [PDF]
We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models.
A Ben-Hur+138 more
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A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations [PDF]
The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$.
Abraham R.+79 more
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Multi-Adaptive Time-Integration [PDF]
Time integration of ODEs or time-dependent PDEs with required resolution of the fastest time scales of the system, can be very costly if the system exhibits multiple time scales of different magnitudes.
Alexander+28 more
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Local discontinuous Galerkin methods for fractional ordinary differential equations [PDF]
This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs).
Deng, Weihua, Hesthaven, Jan S.
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Robust learning with implicit residual networks
In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as the fixed ...
Reshniak, Viktor, Webster, Clayton
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Globally nilpotent differential operators and the square Ising model
We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and ...
Bostan, A.+5 more
core +3 more sources
In this paper, Multirate Partial Differential Equations (MPDEs) are used for the efficient simulation of problems with 2-level pulsed excitations as they often occur in power electronics, e.g., DC-DC switch-mode converters.
Gyselinck, Johan+3 more
core +1 more source
Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system
Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ans\"atze to reduce the classical Lotka-Volterra
Cherniha, Roman, Davydovych, Vasyl'
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Symmetry and Conservation Laws in Semiclassical Wave Packet Dynamics [PDF]
We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether's theorem.
Ohsawa, Tomoki
core +1 more source
Equivalence of variational problems of higher order [PDF]
We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication by a nonzero ...
Doubrov, Boris, Zelenko, Igor
core +2 more sources