A broad class of conservative numerical methods for dispersive wave equations
, 2020 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.
Ketcheson, David I. +2 more
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Stability under Galerkin truncation of A-stable Runge--Kutta semidiscretizations in time [PDF]
, 2017 We consider semilinear evolution equations for which the linear part is normal and generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces.
Wulff, C
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The Norsett time integration methodology for finite element transient analysis
, 2002 This paper presents a set of methods for time integration of problems arising from finite element semidiscretizations. The purpose is to obtain computationally efficient methods which possess higher-order accuracy and controllable dissipation in the ...
MANCUSO, Massimo, Ubertini F.
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Analysis of semidiscretization of the compressible Navier–Stokes equations
Journal of Mathematical Analysis and Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Analysis and Implementation of Numerical Methods for Solving Ordinary Differential Equations [PDF]
, 2017 Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order.
Rana, Muhammad Sohel
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Approximate momentum conservation for spatial semidiscretizations of nonlinear wave equations
, 2002 We prove that a standard second order finite difference uniform space discretization of the nonlinear wave equation with periodic boundary conditions, analytic nonlinearity, and analytic initial data conserves moentum up to an error which is ...
Marcel Oliver +2 more
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Error analysis for discretizations of parabolic problems using continuous finite elements in time and mixed finite elements in space. [PDF]
Numer Math (Heidelb), 2017 Bause M, Radu FA, Köcher U.
europepmc +1 more source
Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach allows the ...
Gassner, Gregor J. +2 more
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Quantile optimization in semidiscrete optimal transport
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study a variant in which the goal is to minimize a quantile of the cost, rather than the mean.
Zhu, Yinchu, Ryzhov, Ilya O.
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Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations [PDF]
, 2017 Wulff, C, Oliver, M, West, M
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