Panopoulos, G. A.; Simos, T. E. An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown. (English) Zbl 1330.65107 J. Comput. Appl. Math. 290, 1-15 (2015). MSC: 65L05 65L06 70F05 PDFBibTeX XMLCite \textit{G. A. Panopoulos} and \textit{T. E. Simos}, J. Comput. Appl. Math. 290, 1--15 (2015; Zbl 1330.65107) Full Text: DOI
Simos, T. E. High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation. (English) Zbl 1403.81016 J. Math. Chem. 50, No. 5, 1224-1261 (2012). MSC: 81Q05 65L05 34L40 49M15 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Math. Chem. 50, No. 5, 1224--1261 (2012; Zbl 1403.81016) Full Text: DOI
Panopoulos, G. A.; Anastassi, Z. A.; Simos, T. E. A symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related IVPs with oscillating solutions. (English) Zbl 1262.65084 Comput. Phys. Commun. 182, No. 8, 1626-1637 (2011). MSC: 65L10 34L40 34A30 65L06 PDFBibTeX XMLCite \textit{G. A. Panopoulos} et al., Comput. Phys. Commun. 182, No. 8, 1626--1637 (2011; Zbl 1262.65084) Full Text: DOI
Simos, T. E. Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation. (English) Zbl 1192.65111 Acta Appl. Math. 110, No. 3, 1331-1352 (2010). MSC: 65L10 34B05 34L40 PDFBibTeX XMLCite \textit{T. E. Simos}, Acta Appl. Math. 110, No. 3, 1331--1352 (2010; Zbl 1192.65111) 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
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
Simos, T. E. A family of four-step trigonometrically-fitted methods and its application to the Schrödinger equation. (English) Zbl 1217.65139 J. Math. Chem. 44, No. 2, 447-466 (2008). MSC: 65L05 81Q05 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Math. Chem. 44, No. 2, 447--466 (2008; Zbl 1217.65139) Full Text: DOI
Simos, T. E. Stabilization of a four-step exonentially-fitted method and its application to the Schrödinger equation. (English) Zbl 1200.65061 Int. J. Mod. Phys. C 18, No. 3, 315-328 (2007). MSC: 65L05 81Q05 65L07 PDFBibTeX XMLCite \textit{T. E. Simos}, Int. J. Mod. Phys. C 18, No. 3, 315--328 (2007; Zbl 1200.65061) Full Text: DOI
Simos, T. E. A four-step exponentially fitted method for the numerical solution of the Schrödinger equation. (English) Zbl 1125.81023 J. Math. Chem. 40, No. 3, 305-318 (2006). MSC: 81Q05 81-08 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Math. Chem. 40, No. 3, 305--318 (2006; Zbl 1125.81023) Full Text: DOI
Simos, T. E.; Vigo-Aguiar, Jesus A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems. (English) Zbl 1196.65123 Comput. Phys. Commun. 152, No. 3, 274-294 (2003). MSC: 65L10 65L12 PDFBibTeX XMLCite \textit{T. E. Simos} and \textit{J. Vigo-Aguiar}, Comput. Phys. Commun. 152, No. 3, 274--294 (2003; Zbl 1196.65123) Full Text: DOI
Kalogiratou, Zacharoula; Simos, T. E. A \(P\)-stable exponentially fitted method for the numerical integration of the Schrödinger equation. (English) Zbl 1023.65080 Appl. Math. Comput. 112, No. 1, 99-112 (2000). MSC: 65L15 65L06 65L20 65L12 34L16 34L40 PDFBibTeX XMLCite \textit{Z. Kalogiratou} and \textit{T. E. Simos}, Appl. Math. Comput. 112, No. 1, 99--112 (2000; Zbl 1023.65080) Full Text: DOI
Simos, T. E. An exponentially fitted eighth-order method for the numerical solution of the Schrödinger equation. (English) Zbl 0956.65063 J. Comput. Appl. Math. 108, No. 1-2, 177-194 (1999). Reviewer: Joerge P.Zubelli (Rio de Janeiro) MSC: 65L10 65L06 65L50 34B30 34L40 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Comput. Appl. Math. 108, No. 1--2, 177--194 (1999; Zbl 0956.65063) Full Text: DOI
Simos, T. E. P-stable exponentially fitted methods for the numerical integration of the Schrödinger equation. (English) Zbl 0924.65073 J. Comput. Phys. 148, No. 2, 305-321 (1999). Reviewer: Jialin Hong (Beijing) MSC: 65L10 34B05 34L15 65L15 34L40 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Comput. Phys. 148, No. 2, 305--321 (1999; Zbl 0924.65073) Full Text: DOI
Simos, T. E. An accurate exponentially-fitted four-step method for the numerical solution of the radial Schrödinger equation. (English) Zbl 0954.65065 Mol. Simul. 20, No. 5, 285-301 (1998). MSC: 65L10 34Lxx 65L06 34B05 34L40 PDFBibTeX XMLCite \textit{T. E. Simos}, Mol. Simul. 20, No. 5, 285--301 (1998; Zbl 0954.65065) Full Text: DOI
Simos, T. E.; Williams, P. S. A finite-difference method for the numerical solution of the Schrödinger equation. (English) Zbl 0877.65054 J. Comput. Appl. Math. 79, No. 2, 189-205 (1997). Reviewer: M.Calvo (Zaragoza) MSC: 65L10 65L06 65L12 34L40 PDFBibTeX XMLCite \textit{T. E. Simos} and \textit{P. S. Williams}, J. Comput. Appl. Math. 79, No. 2, 189--205 (1997; Zbl 0877.65054) Full Text: DOI
Simos, T. E. Exponential fitted methods for the numerical solution of the Schrödinger equation. (English) Zbl 0847.65048 J. Comput. Math. 14, No. 2, 120-134 (1996). Reviewer: I.Coroian (Baia Mare) MSC: 65L06 65L10 34L40 34B15 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Comput. Math. 14, No. 2, 120--134 (1996; Zbl 0847.65048)
Simos, T. E.; Mitsou, G. V. A family of four-step exponential fitted methods for the numerical integration of the radial Schrödinger equation. (English) Zbl 0812.65068 Comput. Math. Appl. 28, No. 4, 41-50 (1994). Reviewer: A.Marciniak (Poznań) MSC: 65L06 65L05 65L20 34B05 34L40 81Q05 PDFBibTeX XMLCite \textit{T. E. Simos} and \textit{G. V. Mitsou}, Comput. Math. Appl. 28, No. 4, 41--50 (1994; Zbl 0812.65068) Full Text: DOI
Simos, T. E.; Raptis, A. D. A fourth-order Bessel fitting method for the numerical solution of the Schrödinger equation. (English) Zbl 0763.65066 J. Comput. Appl. Math. 43, No. 3, 313-322 (1992). Reviewer: T.Regińska (Warszawa) MSC: 65L10 34B05 34L40 PDFBibTeX XMLCite \textit{T. E. Simos} and \textit{A. D. Raptis}, J. Comput. Appl. Math. 43, No. 3, 313--322 (1992; Zbl 0763.65066) Full Text: DOI
Raptis, A. D.; Simos, T. E. A four-step phase-fitted method for the numerical integration of second order initial-value problems. (English) Zbl 0726.65089 BIT 31, No. 1, 160-168 (1991). Reviewer: M.Gousidou-Koutita (Thessaloniki) MSC: 65L06 65L05 34A34 34C25 34L40 PDFBibTeX XMLCite \textit{A. D. Raptis} and \textit{T. E. Simos}, BIT 31, No. 1, 160--168 (1991; Zbl 0726.65089) Full Text: DOI
Simos, T. E. A four-step method for the numerical solution of the Schrödinger equation. (English) Zbl 0705.65050 J. Comput. Appl. Math. 30, No. 3, 251-255 (1990). Reviewer: R.S.Dahiya MSC: 65L05 65L15 34L40 34L15 65L06 PDFBibTeX XMLCite \textit{T. E. Simos}, J. Comput. Appl. Math. 30, No. 3, 251--255 (1990; Zbl 0705.65050) Full Text: DOI