Ueber die numerische Auflösung von Differentialgleichungen

@article{RungeUeberDN,
  title={Ueber die numerische Aufl{\"o}sung von Differentialgleichungen},
  author={Carl Runge},
  journal={Mathematische Annalen},
  volume={46},
  pages={167-178}
}
  • C. Runge
  • Published 1 June 1895
  • Mathematics
  • Mathematische Annalen
Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
TLDR
The method circumvents the need for spatial discretization of the differential operators by proper placement of Gaussian process priors and is an attempt to construct structured and data-efficient learning machines, which are explicitly informed by the underlying physics that possibly generated the observed data.
High order linearly implicit methods for evolution equations: How to solve an ODE by inverting only linear systems
TLDR
This paper introduces a new class of numerical methods for the time integration of evolution equations set as Cauchy problems of ODEs or PDEs that are linearly implicit and have high order, and sets suitable definitions of consistency and stability for these methods.
Numerical contributions for the study of sediment transport beneath tidal bores
Une etude de l'impact des mascarets sur le transport des sediments a l'aide de la simulation numerique a ete realisee dans ce travail. En utilisant le logiciel OpenFOAM CFD, nous avons genere 17
Multi-Fidelity Model Predictive Control of Upstream Energy Production Processes
Multi-Fidelity Model Predictive Control of Upstream Energy Production Processes Ammon Nephi Eaton Department of Chemical Engineering, BYU Doctor of Philosophy Increasing worldwide demand for
Parameter perturbation extrapolation algorithm for Runge-Kutta methods
Abstract In this paper, in order to improve the accuracy of extrapolation Runge-Kutta methods, parameter perturbation is introduced on the basis of extrapolation algorithm, i.e., parameter
Numerical integration of differential-algebraic equations with harmless critical points
Differential-algebraic equations (DAEs) are implicit singular ordinary differential equations, which describe dynamical processes that are restricted by some constraints. In contrast to explicit
Isomeric trees and the order of Runge-Kutta methods
Learning to Assimilate in Chaotic Dynamical Systems
TLDR
Amortized assimilation is introduced, a framework for learning to assimilate in dynamical systems from sequences of noisy observations with no need for ground truth data, and is motivated by powerful results from self-supervised denoising to the dynamical system setting through the use of differentiable simulation.
Statistics of Sliding on Periodic and Atomically Flat Surfaces
Among the so-called analytical models of friction, the most popular and widely used one, the Prandtl-Tomlinson model in one and two dimensions is considered here to numerically describe the sliding
Dynamics of Glyphosate and Aminomethylphosphonic Acid in Soil Under Conventional and Conservation Tillage
This study investigates the adsorption and dissipation of glyphosate and the formation/dissipation of AMPA in non-tilled (NT) and conventionally tilled (CT) soil at 0–5 and 5–20 cm depth. Glyphosate
...
...