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pro vyhledávání: '"65l20"'
In this paper, the stability of IMEX-BDF methods for delay differential equations (DDEs) is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay, $A$ is a positive definite matrix, but $B$ might be any ma
Externí odkaz:
http://arxiv.org/abs/2412.12297
One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of stage solutions without the global Lipschitz continuity assumption of
Externí odkaz:
http://arxiv.org/abs/2412.07321
Computing the numerical solution to high-dimensional tensor differential equations can lead to prohibitive computational costs and memory requirements. To reduce the memory and computational footprint, dynamical low-rank approximation (DLRA) has prov
Externí odkaz:
http://arxiv.org/abs/2412.00858
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