Auzinger, Winfried; Hofstätter, Harald; Koch, Othmar; Quell, Michael Adaptive time propagation for time-dependent Schrödinger equations. (English) Zbl 1469.65116 Int. J. Appl. Comput. Math. 7, No. 1, Paper No. 6, 14 p. (2021). MSC: 65L05 PDFBibTeX XMLCite \textit{W. Auzinger} et al., Int. J. Appl. Comput. Math. 7, No. 1, Paper No. 6, 14 p. (2021; Zbl 1469.65116) Full Text: DOI
Amodio, Pierluigi; Budd, Chris J.; Koch, Othmar; Rottschäfer, Vivi; Settanni, Giuseppina; Weinmüller, Ewa Near critical, self-similar, blow-up solutions of the generalised Korteweg-de Vries equation: asymptotics and computations. (English) Zbl 1453.37064 Physica D 401, Article ID 132179, 16 p. (2020). MSC: 37K40 37K10 35B44 35Q53 65L60 PDFBibTeX XMLCite \textit{P. Amodio} et al., Physica D 401, Article ID 132179, 16 p. (2020; Zbl 1453.37064) Full Text: DOI
Jawecki, Tobias; Auzinger, Winfried; Koch, Othmar Computable upper error bounds for Krylov approximations to matrix exponentials and associated \(\varphi\)-functions. (English) Zbl 1432.65053 BIT 60, No. 1, 157-197 (2020). MSC: 65F60 15A16 65F15 PDFBibTeX XMLCite \textit{T. Jawecki} et al., BIT 60, No. 1, 157--197 (2020; Zbl 1432.65053) Full Text: DOI arXiv
Auzinger, Winfried; Březinová, Iva; Hofstätter, Harald; Koch, Othmar; Quell, Michael Practical splitting methods for the adaptive integration of nonlinear evolution equations. II: Comparisons of local error estimation and step-selection strategies for nonlinear Schrödinger and wave equations. (English) Zbl 07682592 Comput. Phys. Commun. 234, 55-71 (2019). MSC: 65-XX 92-XX PDFBibTeX XMLCite \textit{W. Auzinger} et al., Comput. Phys. Commun. 234, 55--71 (2019; Zbl 07682592) Full Text: DOI
Hofstätter, Harald; Koch, Othmar Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four. (English) Zbl 1408.65042 Numer. Math. 141, No. 3, 681-691 (2019). MSC: 65L05 65L60 PDFBibTeX XMLCite \textit{H. Hofstätter} and \textit{O. Koch}, Numer. Math. 141, No. 3, 681--691 (2019; Zbl 1408.65042) Full Text: DOI arXiv
Auzinger, Winfried; Herfort, Wolfgang; Koch, Othmar; Thalhammer, Mechthild The BCH-formula and order conditions for splitting methods. (English) Zbl 1476.65082 Falcone, Giovanni (ed.), Lie groups, differential equations, and geometry. Advances and surveys. Cham: Springer; Palermo: Università degli Studi di Palermo. UNIPA Springer Ser., 71-83 (2017). MSC: 65J08 68W30 PDFBibTeX XMLCite \textit{W. Auzinger} et al., in: Lie groups, differential equations, and geometry. Advances and surveys. Cham: Springer; Palermo: Università degli Studi di Palermo. 71--83 (2017; Zbl 1476.65082) Full Text: DOI arXiv
Auzinger, Winfried; Koch, Othmar; Quell, Michael Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions. (English) Zbl 1365.65212 Numer. Algorithms 75, No. 1, 261-283 (2017). MSC: 65M20 35K55 65L05 65M12 65M15 PDFBibTeX XMLCite \textit{W. Auzinger} et al., Numer. Algorithms 75, No. 1, 261--283 (2017; Zbl 1365.65212) Full Text: DOI arXiv
Auzinger, Winfried; Hofstätter, Harald; Ketcheson, David; Koch, Othmar Practical splitting methods for the adaptive integration of nonlinear evolution equations. I: Construction of optimized schemes and pairs of schemes. (English) Zbl 1359.65080 BIT 57, No. 1, 55-74 (2017). MSC: 65J08 35Q55 65J15 65M15 PDFBibTeX XMLCite \textit{W. Auzinger} et al., BIT 57, No. 1, 55--74 (2017; Zbl 1359.65080) Full Text: DOI arXiv
Auzinger, Winfried; Herfort, Wolfgang; Hofstätter, Harald; Koch, Othmar Setup of order conditions for splitting methods. (English) Zbl 1453.65115 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 18th international workshop, CASC 2016, Bucharest, Romania, September 19–23, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9890, 30-42 (2016). MSC: 65J08 PDFBibTeX XMLCite \textit{W. Auzinger} et al., Lect. Notes Comput. Sci. 9890, 30--42 (2016; Zbl 1453.65115) Full Text: DOI arXiv Link
Auzinger, Winfried; Kassebacher, Thomas; Koch, Othmar; Thalhammer, Mechthild Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime. (English) Zbl 1338.65214 Numer. Algorithms 72, No. 1, 1-35 (2016). MSC: 65M06 35Q55 65M12 65M15 PDFBibTeX XMLCite \textit{W. Auzinger} et al., Numer. Algorithms 72, No. 1, 1--35 (2016; Zbl 1338.65214) Full Text: DOI arXiv Link
Auzinger, Winfried; Koch, Othmar; Thalhammer, Mechthild Defect-based local error estimators for high-order splitting methods involving three linear operators. (English) Zbl 1325.65131 Numer. Algorithms 70, No. 1, 61-91 (2015). MSC: 65M15 35K90 65J08 35Q55 PDFBibTeX XMLCite \textit{W. Auzinger} et al., Numer. Algorithms 70, No. 1, 61--91 (2015; Zbl 1325.65131) Full Text: DOI Link
Amodio, P.; Budd, C. J.; Koch, O.; Settanni, G.; Weinmüller, E. Asymptotical computations for a model of flow in saturated porous media. (English) Zbl 1334.76148 Appl. Math. Comput. 237, 155-167 (2014). MSC: 76S05 PDFBibTeX XMLCite \textit{P. Amodio} et al., Appl. Math. Comput. 237, 155--167 (2014; Zbl 1334.76148) Full Text: DOI Link
Auzinger, Winfried; Koch, Othmar; Bagherzadeh, Amir Saboor Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations. (English) Zbl 1311.65104 BIT 54, No. 4, 873-900 (2014). Reviewer: Alexandru Mihai Bica (Oradea) MSC: 65L70 65L10 65L60 34B05 34B15 65L12 65L20 PDFBibTeX XMLCite \textit{W. Auzinger} et al., BIT 54, No. 4, 873--900 (2014; Zbl 1311.65104) Full Text: DOI Link
Hofstätter, Harald; Koch, Othmar An approximate eigensolver for self-consistent field calculations. (English) Zbl 1317.65098 Numer. Algorithms 66, No. 3, 609-641 (2014). Reviewer: Martin Plešinger (Liberec) MSC: 65F15 65F08 65Z05 65Y05 PDFBibTeX XMLCite \textit{H. Hofstätter} and \textit{O. Koch}, Numer. Algorithms 66, No. 3, 609--641 (2014; Zbl 1317.65098) Full Text: DOI
Higueras, Inmaculada; Happenhofer, Natalie; Koch, Othmar; Kupka, Friedrich Optimized strong stability preserving IMEX Runge-Kutta methods. (English) Zbl 1294.65076 J. Comput. Appl. Math. 272, 116-140 (2014). MSC: 65L06 65L05 34A34 65M20 35L60 65L20 85A05 PDFBibTeX XMLCite \textit{I. Higueras} et al., J. Comput. Appl. Math. 272, 116--140 (2014; Zbl 1294.65076) Full Text: DOI
Auzinger, Winfried; Koch, Othmar; Thalhammer, Mechthild Defect-based local error estimators for splitting methods, with application to Schrödinger equations. II: Higher-order methods for linear problems. (English) Zbl 1291.65282 J. Comput. Appl. Math. 255, 384-403 (2014). MSC: 65M15 65M12 35Q41 65J10 PDFBibTeX XMLCite \textit{W. Auzinger} et al., J. Comput. Appl. Math. 255, 384--403 (2014; Zbl 1291.65282) Full Text: DOI
Dick, Alexander; Koch, Othmar; März, Roswitha; Weinmüller, Ewa Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point. (English) Zbl 1262.65092 Math. Comput. 82, No. 282, 893-918 (2013). MSC: 65L80 65L60 65L20 65L70 34A09 PDFBibTeX XMLCite \textit{A. Dick} et al., Math. Comput. 82, No. 282, 893--918 (2013; Zbl 1262.65092) Full Text: DOI
Kupka, Friedrich; Happenhofer, Natalie; Higueras, Inmaculada; Koch, Othmar Total-variation-diminishing implicit-explicit Runge-Kutta methods for the simulation of double-diffusive convection in astrophysics. (English) Zbl 1241.85010 J. Comput. Phys. 231, No. 9, 3561-3586 (2012). MSC: 85A30 85-08 76E20 PDFBibTeX XMLCite \textit{F. Kupka} et al., J. Comput. Phys. 231, No. 9, 3561--3586 (2012; Zbl 1241.85010) Full Text: DOI arXiv
Auzinger, Winfried; Koch, Othmar; Thalhammer, Mechthild Defect-based local error estimators for splitting methods, with application to Schrödinger equations. I: The linear case. (English) Zbl 1238.65091 J. Comput. Appl. Math. 236, No. 10, 2643-2659 (2012). MSC: 65M15 35Q41 65M99 PDFBibTeX XMLCite \textit{W. Auzinger} et al., J. Comput. Appl. Math. 236, No. 10, 2643--2659 (2012; Zbl 1238.65091) Full Text: DOI
Blaha, P.; Hofstätter, H.; Koch, O.; Laskowski, R.; Schwarz, K. Iterative diagonalization in augmented plane wave based methods in electronic structure calculations. (English) Zbl 1183.82003 J. Comput. Phys. 229, No. 2, 453-460 (2010). MSC: 82B10 65F15 65F10 65Z05 PDFBibTeX XMLCite \textit{P. Blaha} et al., J. Comput. Phys. 229, No. 2, 453--460 (2010; Zbl 1183.82003) Full Text: DOI
Koch, Othmar; Kreuzer, Wolfgang; Scrinzi, Armin Approximation of the time-dependent electronic Schrödinger equation by MCTDHF. (English) Zbl 1088.65092 Appl. Math. Comput. 173, No. 2, 960-976 (2006). MSC: 65M70 35Q40 81Q05 65M20 PDFBibTeX XMLCite \textit{O. Koch} et al., Appl. Math. Comput. 173, No. 2, 960--976 (2006; Zbl 1088.65092) Full Text: DOI