Search Results - "Othmar Koch"

Total-variation-diminishing implicit–explicit Runge–Kutta methods for the simulation of double-diffusive convection in astrophysics by Kupka, Friedrich, Happenhofer, Natalie, Higueras, Inmaculada, Koch, Othmar

“…We put forward the use of total-variation-diminishing (or more generally, strong stability preserving) implicit–explicit Runge–Kutta methods for the time…”
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Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part II: Comparisons of local error estimation and step-selection strategies for nonlinear Schrödinger and wave equations by Auzinger, Winfried, Březinová, Iva, Hofstätter, Harald, Koch, Othmar, Quell, Michael

“…We compare the practical performance of adaptive splitting methods for the solution of nonlinear Schrödinger equations. Different methods for local error…”
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Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point by Alexander Dick, Othmar Koch, Roswitha März, Ewa Weinmüller

“…singularity of the first kind and apply polynomial collocation to the . We show that for a certain class of well-posed boundary value problems in DAEs having a…”
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Collocation methods for index 1 DAEs with a singularity of the first kind by KOCH, OTHMAR, MÄRZ, ROSWITHA, PRAETORIUS, DIRK, WEINMÜLLER, EWA

“…singularity of the first kind, apply polynomial collocation to the original DAE system and consider different choices of the collocation points such as…”
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Approximation of the time-dependent electronic Schrödinger equation by MCTDHF by Koch, Othmar, Kreuzer, Wolfgang, Scrinzi, Armin

“…The numerical approximation of the solution of the time-dependent Schrödinger equation arising in ultrafast laser dynamics is discussed. The linear electronic…”
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Efficient computation of the MCTDHF approximation to the time-dependent Schrödinger equation by Othmar Koch

“…We discuss analytical and numerical properties of the multi-configuration time-dependent Hartree-Fock method for the approximate solution of the time-dependent…”
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Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four by Hofstätter, Harald, Koch, Othmar

“…We consider commutator-free exponential integrators as put forward in Alverman and Fehske (J Comput Phys 230:5930–5956, 2011 ). For parabolic problems, it is…”
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The convergence of shooting methods for singular boundary value problems by KOCH, Othmar, WEINMÜLLER, Ewa B

“…We investigate the convergence properties of single and multiple shooting when applied to singular boundary value problems. Particular attention is paid to the…”
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Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations by Winfried Auzinger, Ernst Karner, Othmar Koch, Ewa Weinmüller

“…We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation…”
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Computable upper error bounds for Krylov approximations to matrix exponentials and associated φ-functions by Jawecki, Tobias, Auzinger, Winfried, Koch, Othmar

“…An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual)…”
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Computable upper error bounds for Krylov approximations to matrix exponentials and associated $${\varvec{\varphi }}$$-functions by Jawecki, Tobias, Auzinger, Winfried, Koch, Othmar

“…An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual)…”
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Optimized strong stability preserving IMEX Runge–Kutta methods by Higueras, Inmaculada, Happenhofer, Natalie, Koch, Othmar, Kupka, Friedrich

“…We construct and analyze robust strong stability preserving IMplicit–EXplicit Runge–Kutta (IMEX RK) methods for models of flow with diffusion as they appear in…”
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Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part II. Higher-order methods for linear problems by Auzinger, Winfried, Koch, Othmar, Thalhammer, Mechthild

“…In this work, defect-based local error estimators for higher-order exponential operator splitting methods are constructed and analyzed in the context of…”
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Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions by Auzinger, Winfried, Koch, Othmar, Quell, Michael

“…We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic…”
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Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes by Auzinger, Winfried, Hofstätter, Harald, Ketcheson, David, Koch, Othmar

“…We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution…”
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Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime by Auzinger, Winfried, Hofstätter, Harald, Koch, Othmar, Kropielnicka, Karolina, Singh, Pranav

“…Time dependent Schrödinger equations with conservative force field commonly constitute a major challenge in the numerical approximation, especially when they…”
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Near critical, self-similar, blow-up solutions of the generalised Korteweg–de Vries equation: Asymptotics and computations by Amodio, Pierluigi, Budd, Chris J., Koch, Othmar, Rottschäfer, Vivi, Settanni, Giuseppina, Weinmüller, Ewa

“…In this article we give a detailed asymptotic analysis of the near critical self-similar blowup solutions to the Generalised Korteweg–de Vries equation (GKdV)…”
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Defect-based local error estimators for high-order splitting methods involving three linear operators by Auzinger, Winfried, Koch, Othmar, Thalhammer, Mechthild

“…Prior work on high-order exponential operator splitting methods is extended to evolution equations defined by three linear operators. A posteriori local error…”
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Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part III: The nonlinear case by Auzinger, Winfried, Hofstätter, Harald, Koch, Othmar, Thalhammer, Mechthild

“…The present work is concerned with the efficient time integration of nonlinear evolution equations by exponential operator splitting methods. Defect-based…”
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Computable upper error bounds for Krylov approximations to matrix exponentials and associated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\varphi }}$$\end{document}φ-functions by Jawecki, Tobias, Auzinger, Winfried, Koch, Othmar

“…An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual)…”
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