Search Results - "Winfried Auzinger"

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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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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Adaptive Time Propagation for Time-dependent Schrödinger equations by Auzinger, Winfried, Hofstätter, Harald, Koch, Othmar, Quell, Michael

“…We compare adaptive time integrators for the numerical solution of linear Schrödinger equations where the Hamiltonian explicitly depends on time. The…”
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Local error structures and order conditions in terms of Lie elements for exponential splitting schemes by Auzinger, Winfried, Herfort, Wolfgang

“…We discuss the structure of the local error of exponential operator splitting methods. In particular, it is shown that the leading error term is a Lie element,…”
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Convergence of rational multistep methods of Adams-Padé type by Auzinger, Winfried, Łapińska, Magdalena

“…Rational generalizations of multistep schemes, where the linear stiff part of a given problem is treated by an A -stable rational approximation, have been…”
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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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A uniform quantitative stiff stability estimate for BDF schemes by Winfried Auzinger, Wolfgang Herfort

“…The concepts of stability regions, \(A\)- and \(A(\alpha)\)-stability - albeit based on scalar models - turned out to be essential for the identification of…”
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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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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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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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On nonlinear singular BVPs with nonsmooth data. Part 2: Convergence of collocation methods by Auer, Felix Karl, Auzinger, Winfried, Burkotová, Jana, Rachůnková, Irena, Weinmüller, Ewa B.

“…We discuss numerical solution of boundary value problems for systems of nonlinear ordinary differential equations with a time…”
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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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Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime by Auzinger, Winfried, Kassebacher, Thomas, Koch, Othmar, Thalhammer, Mechthild

“…The error behavior of exponential operator splitting methods for nonlinear Schrödinger equations in the semiclassical regime is studied. For the Lie and Strang…”
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Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I: The linear case by Auzinger, Winfried, Koch, Othmar, Thalhammer, Mechthild

“…We introduce a defect correction principle for exponential operator splitting methods applied to time-dependent linear Schrödinger equations and construct a…”
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Shooting methods for state-dependent impulsive boundary value problems, with applications by Auzinger, Winfried, Burkotová, Jana, Rachůnková, Irena, Wenin, Victor

“…For impulsive boundary value problems whose solutions encounter discontinuities (jumps) at a priori not known positions depending on the solution itself,…”
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Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations by Auzinger, Winfried, Koch, Othmar, Saboor Bagherzadeh, Amir

“…We investigate efficient asymptotically correct a posteriori error estimates for the numerical approximation of two-point boundary value problems for second…”
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