Cieśliński, Jan L.; Ratkiewicz, Bogusław Discrete gradient algorithms of high order for one-dimensional systems. (English) Zbl 1264.65207 Comput. Phys. Commun. 183, No. 3, 617-627 (2012). MSC: 65P10 37M15 PDFBibTeX XMLCite \textit{J. L. Cieśliński} and \textit{B. Ratkiewicz}, Comput. Phys. Commun. 183, No. 3, 617--627 (2012; Zbl 1264.65207) Full Text: DOI arXiv
Konguetsof, A. A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation. (English) Zbl 1304.65170 J. Math. Chem. 49, No. 7, 1330-1356 (2011). MSC: 65L05 65L06 PDFBibTeX XMLCite \textit{A. Konguetsof}, J. Math. Chem. 49, No. 7, 1330--1356 (2011; Zbl 1304.65170) Full Text: DOI
Kosmas, O. T.; Vlachos, D. S. Phase-fitted discrete Lagrangian integrators. (English) Zbl 1205.65326 Comput. Phys. Commun. 181, No. 3, 562-568 (2010). MSC: 65P10 37M15 PDFBibTeX XMLCite \textit{O. T. Kosmas} and \textit{D. S. Vlachos}, Comput. Phys. Commun. 181, No. 3, 562--568 (2010; Zbl 1205.65326) Full Text: DOI arXiv
Konguetsof, A. Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation. (English) Zbl 1198.81092 J. Math. Chem. 48, No. 2, 224-252 (2010). MSC: 81Q05 81T80 65L06 PDFBibTeX XMLCite \textit{A. Konguetsof}, J. Math. Chem. 48, No. 2, 224--252 (2010; Zbl 1198.81092) Full Text: DOI
Konguetsof, A. A new two-step hybrid method for the numerical solution of the Schrödinger equation. (English) Zbl 1200.81051 J. Math. Chem. 47, No. 2, 871-890 (2010). MSC: 81Q05 81T80 81-08 34L40 PDFBibTeX XMLCite \textit{A. Konguetsof}, J. Math. Chem. 47, No. 2, 871--890 (2010; Zbl 1200.81051) Full Text: DOI
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E. Computation of the eigenvalues of the Schrödinger equation by exponentially-fitted Runge-Kutta-Nyström methods. (English) Zbl 1198.81088 Comput. Phys. Commun. 180, No. 2, 167-176 (2009). MSC: 81Q05 65L15 65L06 PDFBibTeX XMLCite \textit{Z. Kalogiratou} et al., Comput. Phys. Commun. 180, No. 2, 167--176 (2009; Zbl 1198.81088) Full Text: DOI
Simos, T. E. P-stability, trigonometric-fitting and the numerical solution of the radial Schrödinger equation. (English) Zbl 1198.81103 Comput. Phys. Commun. 180, No. 7, 1072-1085 (2009). MSC: 81Q05 PDFBibTeX XMLCite \textit{T. E. Simos}, Comput. Phys. Commun. 180, No. 7, 1072--1085 (2009; Zbl 1198.81103) Full Text: DOI
Vlachos, D. S.; Anastassi, Z. A.; Simos, T. E. High order phase fitted multistep integrators for the Schrödinger equation with improved frequency tolerance. (English) Zbl 1200.81057 J. Math. Chem. 46, No. 4, 1009-1049 (2009). MSC: 81Q05 81T80 34L40 81-08 PDFBibTeX XMLCite \textit{D. S. Vlachos} et al., J. Math. Chem. 46, No. 4, 1009--1049 (2009; Zbl 1200.81057) Full Text: DOI arXiv
Anastassi, Z. A.; Vlachos, D. S.; Simos, T. E. A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems. (English) Zbl 1200.81045 J. Math. Chem. 46, No. 4, 1158-1171 (2009). MSC: 81Q05 34L40 81T80 81-08 65L06 PDFBibTeX XMLCite \textit{Z. A. Anastassi} et al., J. Math. Chem. 46, No. 4, 1158--1171 (2009; Zbl 1200.81045) Full Text: DOI arXiv
Simos, T. E. A new Numerov-type method for the numerical solution of the Schrödinger equation. (English) Zbl 1183.81060 J. Math. Chem. 46, No. 3, 981-1007 (2009). MSC: 81Q05 65G20 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Math. Chem. 46, No. 3, 981--1007 (2009; Zbl 1183.81060) Full Text: DOI
Vlachos, D. S.; Anastassi, Z. A.; Simos, T. E. High order multistep methods with improved phase-lag characteristics for the integration of the Schrödinger equation. (English) Zbl 1198.81106 J. Math. Chem. 46, No. 2, 692-725 (2009). MSC: 81Q05 81-08 81T80 PDFBibTeX XMLCite \textit{D. S. Vlachos} et al., J. Math. Chem. 46, No. 2, 692--725 (2009; Zbl 1198.81106) Full Text: DOI arXiv
Anastassi, Z. A.; Vlachos, D. S.; Simos, T. E. A new methodology for the construction of numerical methods for the approximate solution of the Schrödinger equation. (English) Zbl 1198.81077 J. Math. Chem. 46, No. 2, 652-691 (2009). MSC: 81Q05 81-08 81T80 PDFBibTeX XMLCite \textit{Z. A. Anastassi} et al., J. Math. Chem. 46, No. 2, 652--691 (2009; Zbl 1198.81077) Full Text: DOI
Anastassi, Z. A.; Vlachos, D. S.; Simos, T. E. A new methodology for the development of numerical methods for the numerical solution of the Schrödinger equation. (English) Zbl 1198.81076 J. Math. Chem. 46, No. 2, 621-651 (2009). MSC: 81Q05 81-08 81T80 PDFBibTeX XMLCite \textit{Z. A. Anastassi} et al., J. Math. Chem. 46, No. 2, 621--651 (2009; Zbl 1198.81076) Full Text: DOI arXiv
Panopoulos, G. A.; Anastassi, Z. A.; Simos, T. E. Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions. (English) Zbl 1198.81099 J. Math. Chem. 46, No. 2, 604-620 (2009). MSC: 81Q05 81V45 34L40 81T80 PDFBibTeX XMLCite \textit{G. A. Panopoulos} et al., J. Math. Chem. 46, No. 2, 604--620 (2009; Zbl 1198.81099) Full Text: DOI arXiv
Anastassi, Z. A.; Simos, T. E. A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution. (English) Zbl 1198.81075 J. Math. Chem. 45, No. 4, 1102-1129 (2009). MSC: 81Q05 65D30 81T80 PDFBibTeX XMLCite \textit{Z. A. Anastassi} and \textit{T. E. Simos}, J. Math. Chem. 45, No. 4, 1102--1129 (2009; Zbl 1198.81075) Full Text: DOI
Simos, T. E. High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation. (English) Zbl 1161.65091 Appl. Math. Comput. 209, No. 1, 137-151 (2009). MSC: 65P10 37M15 PDFBibTeX XMLCite \textit{T. E. Simos}, Appl. Math. Comput. 209, No. 1, 137--151 (2009; Zbl 1161.65091) Full Text: DOI
Simos, T. E. Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation. (English) Zbl 1217.65054 J. Math. Chem. 44, No. 2, 483-499 (2008). MSC: 65D30 81Q05 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Math. Chem. 44, No. 2, 483--499 (2008; Zbl 1217.65054) Full Text: DOI