Numerical Methods for Ordinary Differential Equations

By Brian D. Storey. 1989

Subfields: Optimization & Training, Numerical Methods & Scientific Computing

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Citations in the corpus

The Numerics of GANs (2017, methodology): “It can be shown that the implicit Euler method has appealing stability properties [7] that can be translated into convergence theorems for local Nash-equilibria.”
Geometric integrators for ODEs (2006, methodology): “Runge–Kutta (RK) methods are defined for systems with linear phase space R [21].”
A review of numerical methods for nonlinear partial differential equations (2012, unknown): “The solution of such semidiscrete systems is obtained by standard ODE solvers [82, 96, 97, 28].”
Statistical Learning by Imitation of Competing Constraints in Joint Space and Task Space (2009, methodology): “where t refers to the time elapsed from the beginning of the demonstration (note, however, that other numerical methods for ordinary differential equations can similarly be used here [17]).”
Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers (2021, methodology): “We discuss a few of the simplest methods, which are first-order methods with local error O(h(2)) [6].”
B-SERIES METHODS CANNOT BE VOLUME-PRESERVING (2007, background): “This differentialequation construction in the discussion below is based on the construction in [2].”
Spectral Deferred Correction Methods for Ordinary Differential Equations (2000, background): “The construction of efficient, stable and high order methods for solving initial value problems governed by systems of ordinary differential equations (ODEs) is, in many respects, a mature subject [1, 2, 6, 9, 10, 13].”
CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model (2012, unknown): “The Butcher tableau (Butcher 2003) for N ¼ 5 is given by”
Numerical Methods for Ordinary Differential Equations (2018, methodology): “3 Consistency and order of accuracy Given a Runge–Kutta method, how do we determine its order? How do we construct a method which is, say, pth order accurate? How many stages s are required for a pth order explicit Runge–Kutta method? The first question is actually not so easy to answer; the second ”
Accelerated Mirror Descent in Continuous and Discrete Time (2015, methodology): “Using a mixed forward/backward Euler scheme (see e.g. Chapter 2 in [10]), we can discretize the ODE system (5) using a step size √ s as follows.”
RUNGE-KUTTA SCHEMES FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS (2014, methodology): “From, for example, Section 322, page 175 in [3], we know that c4 = 1 necessarily.”
Generative Adversarial Networks (GANs) (2020, methodology): “40 overcome above-mentioned issues, researchers have proposed several evaluation methods for GANs [154][155].”
Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations (2008, methodology): “In the following proofs we consider the A-stability of ordinary differential equations [1,4].”
Modeling and Simulation of Genetic Regulatory Systems: A Literature Review (2002, unknown): “In numerical simulation , the exact solution of the equations is approximated by calculating approximate values x 0 ; : : : ; x m for x at consecutive time-points t 0 ; : : : ; t m (Lambert, 1991).”