Zobrazeno 1 - 10
of 90
pro vyhledávání: '"65L03"'
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
Autor:
Ando', Alessia, Vermiglio, Rossana
Exponential Runge-Kutta methods for semilinear ordinary differential equations can be extended to abstract differential equations, defined on Banach spaces. Thanks to the sun-star theory, both delay differential equations and renewal equations can be
Externí odkaz:
http://arxiv.org/abs/2410.00498
Autor:
Pulch, Roland
We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its stationary solutio
Externí odkaz:
http://arxiv.org/abs/2408.09861
Autor:
Huang, Qiumei, Zhu, Qiao
This paper presents the double-activation neural network (DANN), a novel network architecture designed for solving parabolic equations with time delay. In DANN, each neuron is equipped with two activation functions to augment the network's nonlinear
Externí odkaz:
http://arxiv.org/abs/2405.08690
In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the reference d
Externí odkaz:
http://arxiv.org/abs/2403.08597
Autor:
Provoost, Evert, Michiels, Wim
We reformulate the Lanczos tau method for the discretization of time-delay systems in terms of a pencil of operators, allowing for new insights into this approach. As a first main result, we show that, for the choice of a shifted Legendre basis, this
Externí odkaz:
http://arxiv.org/abs/2403.03895
Publikováno v:
J. Sci. Comput. 99 (2024) 48
In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild hypotheses,
Externí odkaz:
http://arxiv.org/abs/2310.10526
Autor:
andò, Alessia, Breda, Dimitri
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and provide a the
Externí odkaz:
http://arxiv.org/abs/2305.12186
To our knowledge, the existing measure approximation theory requires the diffusion term of the stochastic delay differential equations (SDDEs) to be globally Lipschitz continuous. Our work is to develop a new explicit numerical method for SDDEs with
Externí odkaz:
http://arxiv.org/abs/2303.05702
Autor:
Ghoreishi, F., Ghaffari, R.
This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total differential for
Externí odkaz:
http://arxiv.org/abs/2210.13138