This breakthrough radically changes the understanding of one of the oldest areas of mathematics, crucial to fundamental physics and economics ...

The development of humans and other animals unfolds gradually over time, with cells taking on specific roles and functions ...

Abstract: Analytically solving complex or large-scale differential equations is often difficult or even impossible, making numerical integration methods indispensable. However, as all numerical ...

ABSTRACT: This paper investigates the emergence and transformation of self-oscillatory regimes in a nonlinear dynamic system based on a generalized van der Pol oscillator model. Using asymptotic and ...

Abstract: Neural Ordinary Differential Equations (NODEs) revolutionize the way we view residual networks as solvers for initial value problems (IVPs), with layer depth serving as the time step. In ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. In chemical reaction network theory, ordinary differential equations are used to model ...

This paper is dedicated to the proposition that, in order to take full advantage for real-time computations of highly parallel computers as can be expected to be available in the near future, much of ...

This course provides an introduction to topics involving ordinary differential equations. Emphasis is placed on the development of abstract concepts and applications for first-order and linear ...

An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, ...