Zobrazeno 1 - 10
of 911
pro vyhledávání: '"65L20"'
We study the connections between ordinary differential equations and optimization algorithms in a non-Euclidean setting. We propose a novel accelerated algorithm for minimising convex functions over a convex constrained set. This algorithm is a natur
Externí odkaz:
http://arxiv.org/abs/2410.19380
Autor:
Ando', Alessia, Sieber, Jan
We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that are not lo
Externí odkaz:
http://arxiv.org/abs/2410.07375
A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some parameterized I
Externí odkaz:
http://arxiv.org/abs/2410.06463
Autor:
Fiedler, Bernold
In the present paper, the simplest scalar ODE case is studied for polynomials $$ \dot{w}=f(w)=(w-e_0)\cdot\ldots\cdot(w-e_{d-1}) $$ of degree $d$ with $d$ simple complex zeros. The explicit solution by separation of variables and explicit integration
Externí odkaz:
http://arxiv.org/abs/2410.05043
In this article, we study the explosion time of the solution to autonomous stochastic differential equations driven by the fractional Brownian motion with Hurst parameter $H>1/2$. With the help of the Lamperti transformation, we are able to tackle th
Externí odkaz:
http://arxiv.org/abs/2410.00581
To solve the Cahn-Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the implicit system a
Externí odkaz:
http://arxiv.org/abs/2409.17736
Autor:
Popov, I. S.
Publikováno v:
J. Sci. Comput. 100, 22 (2024)
An adaptation of the arbitrary high order ADER-DG numerical method with local DG predictor for solving the IVP for a first-order non-linear ODE system is proposed. The proposed numerical method is a completely one-step ODE solver with uniform steps,
Externí odkaz:
http://arxiv.org/abs/2409.09933
We present a stability analysis of Physics-Informed Neural Networks (PINNs) coupled with random projections, for the numerical solution of (stiff) linear differential equations. For our analysis, we consider systems of linear ODEs, and linear parabol
Externí odkaz:
http://arxiv.org/abs/2408.15393
Publikováno v:
Journal of Computational Physics, 2024, 519: 113456
Explicit integrating factor Runge-Kutta methods are attractive and popular in developing high-order maximum bound principle preserving time-stepping schemes for Allen-Cahn type gradient flows. However, they always suffer from the non-preservation of
Externí odkaz:
http://arxiv.org/abs/2408.14984
We present two new approaches for point prediction with streaming data. One is based on the Count-Min sketch (CMS) and the other is based on Gaussian process priors with a random bias. These methods are intended for the most general predictive proble
Externí odkaz:
http://arxiv.org/abs/2408.01318