Results 31 to 40 of about 167 (129)
A broad class of conservative numerical methods for dispersive wave equations
, 2021 We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time.
Dimitrios Mitsotakis (8510154) +2 more
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Semidiscrete Toda lattices [PDF]
Theoretical and Mathematical Physics, 2012 15 ...
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Stability and accuracy of difference schemes for hyperbolic problems
, 1985 Bounds for the error order and error constant of full- and semidiscretizations of hyperbolic problems are given. In order to be able to compare fulldiscretizations a scaling is introduced.
Jeltsch, Rolf
core +1 more source
A-stable Runge-Kutta methods for semilinear evolution equations [PDF]
, 2017 We consider semilinear evolution equations for which the linear part generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces.
Wulff, C, Oliver, M
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A numerical study of variational discretizations of the Camassa–Holm equation
, 2021 We present two semidiscretizations of the Camassa–Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an existing conservative multipeakon method on the real line, for which we ...
Galtung, Sondre Tesdal, Grunert, Katrin
core
Finite and Infinitesimal Flexibility of Semidiscrete Surfaces [PDF]
Arnold Mathematical Journal, 2015 In this paper we study infinitesimal and finite flexibility for generic semidiscrete surfaces. We prove that generic 2-ribbon semidiscrete surfaces have one degree of infinitesimal and finite flexibility. In particular we write down a system of differential equations describing isometric deformations in the case of existence.
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Numerical Methods for Partial Differential Equations, Volume 41, Issue 4, July 2025.ABSTRACT We develop structure‐preserving numerical methods for the Serre–Green–Naghdi equations, a model for weakly dispersive free‐surface waves. We consider both the classical form, requiring the inversion of a nonlinear elliptic operator, and a hyperbolic approximation of the equations, allowing fully explicit time stepping.
H. Ranocha, M. Ricchiuto
wiley +1 more source
Flow Matching with Semidiscrete Couplings
CoRRFlow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points $(\mathbf{x}_0,\mathbf{x}_1)$ and ensuring that the velocity field is aligned, on average, with $\mathbf{x}_1-\mathbf{x}_0$ when ...
Alireza Mousavi Hosseini +3 more
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Step Sizes for Strong Stability Preservation with Downwind-Biased Operators [PDF]
, 2011 Strong stability preserving (SSP) integrators for initial value ODEs preserve temporal monotonicity solution properties in arbitrary norms. All existing SSP methods, including implicit methods, either require small step sizes or achieve only first order ...
Ketcheson, David I., David I. Ketcheson
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 8, Page 8793-8805, 30 May 2025.ABSTRACT We study a class of models for nonlinear acoustics, including the well‐known Westervelt and Kuznetsov equations, as well as a model of Rasmussen that can be seen as a thermodynamically consistent modification of the latter. Using linearization, energy estimates, and fixed‐point arguments, we establish the existence and uniqueness of solutions ...
Herbert Egger, Marvin Fritz
wiley +1 more source