On the Partial Difference Equations, of Mathematical Physics

By R. Courant, K. Friedrichs, H. Lewy. 2015

2,216 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f623f28e57448218a44e2f16e2a5e5161b008ec0

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In Numerical Analysis

Citations in the corpus

A domain decomposition approach to implementing fault slip in finite‐element models of quasi‐static and dynamic crustal deformation (2013, methodology): “[48] In dynamic simulations, the Courant-FriderichsLewy condition [Courant et al., 1967] controls the stability of the explicit time integration.”
Communication-Efficient and Distributed Learning Over Wireless Networks: Principles and Applications (2020, methodology): “, xn}, the discretization step size Δt should satisfy Δt ≤ ( n i=1 1/xi) −1 according to the Courant–Friedrichs–Lewy condition [159].”
Towards a generalised GPU/CPU shallow-flow modelling tool (2013, methodology): “3 Stability criterion The maximum permissible timestep for stability in the scheme is governed by the work of Courant-Friedrichs-Lewy Courant et al. (1967) and given by lowest instance from all cells of”
Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes (2013, background): “The Courant-Friedrichs-Lewy (CFL) condition [57], required for stability, imposes an upper limit on the time step.”
Anomalous dissipation for 1/5-Hölder Euler flows (2015, methodology): “[5]), restricting the coarse-grained flow to times of the order of ‖∇v‖−1 0 , cf.”
r.avaflow v1, an advanced open-source computational framework for the propagation and interaction of two-phase mass flows (2016, neutral): “The time step length 1t is dynamically updated according to the CFL condition (Courant et al., 1967; Tai et al., 2002; Wang et al., 2004).”
Message Passing Neural PDE Solvers (2022, background): “Solving these differential equations is of huge importance for problems in all numerate disciplines such as weather forecasting (Lynch, 2008), astronomical simulations (Courant et al., 1967), molecular modeling (Leli`evre & Stoltz, 2016) , or jet engine design (Athanasopoulos et al., 2009).”
Choose a Transformer: Fourier or Galerkin (2021, methodology): “Traditional methods, such as finite element/difference [20, 22], spectral methods [12], etc.”
pyGIMLi: An open-source library for modelling and inversion in geophysics (2017, methodology): “The whole simulation time is 12 days in summary and we used 1600 time steps to ful ﬁ ll the Courant-Friedrichs-Lewy condition (Courant et al., 1967) ensuring the particle movement does not exceed cell dimensions within one time step.”
Assessing the utility of social media as a data source for flood risk management using a real‐time modelling framework (2017, methodology): “Consequently, the explicit models are constrained by the Courant–Friedrichs–Lewy condition (Courant et al., 1967), which is a function of the largest velocity within the domain and the cell dimensions; accordingly, if the cell resolution of these models is halved, the simulation run-time can be expe”
A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications (2015, methodology): “Since the discretization given by equations (3) and (4) is explicit in time, it is subject to a Courant-FriedrichsLewy (CFL) stability constraint over the computational time step [Courant et al., 1967].”
Massive Autonomous UAV Path Planning: A Neural Network Based Mean-Field Game Theoretic Approach (2019, methodology): “While effective, MFG theoretic methods are computationally expensive due to solving HJB and FPK equations, limiting their adoption for real-time multi-dimensional control applications [6].”
Comparing the Markov Chain Model with the Eulerian and Lagrangian Models for Indoor Transient Particle Transport Simulations (2015, background): “, the Courant number is less than 1 (Courant et al. 1928).”