Ehigie, Julius O.; Luan, Vu Thai; Okunuga, Solomon A.; You, Xiong Exponentially fitted two-derivative DIRK methods for oscillatory differential equations. (English) Zbl 1510.65143 Appl. Math. Comput. 418, Article ID 126770, 23 p. (2022). MSC: 65L06 34C10 PDFBibTeX XMLCite \textit{J. O. Ehigie} et al., Appl. Math. Comput. 418, Article ID 126770, 23 p. (2022; Zbl 1510.65143) Full Text: DOI arXiv
D’Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice Adapted numerical modeling for advection-reaction-diffusion problems on a bidimensional spatial domain. (English) Zbl 1473.65100 Int. J. Math. Comput. Sci. 16, No. 4, 1803-1829 (2021). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{R. D'Ambrosio} et al., Int. J. Math. Comput. Sci. 16, No. 4, 1803--1829 (2021; Zbl 1473.65100) Full Text: Link
Fang, Yonglei; Yang, Yanping; You, Xiong An explicit trigonometrically fitted Runge-Kutta method for stiff and oscillatory problems with two frequencies. (English) Zbl 1480.65161 Int. J. Comput. Math. 97, No. 1-2, 85-94 (2020). MSC: 65L04 65L05 65L06 PDFBibTeX XMLCite \textit{Y. Fang} et al., Int. J. Comput. Math. 97, No. 1--2, 85--94 (2020; Zbl 1480.65161) Full Text: DOI
Chen, Zhaoxia; Shi, Lei; Liu, Siyao; You, Xiong Trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for second-order oscillatory differential equations. (English) Zbl 1477.65110 Appl. Numer. Math. 142, 171-189 (2019). MSC: 65L06 65L05 PDFBibTeX XMLCite \textit{Z. Chen} et al., Appl. Numer. Math. 142, 171--189 (2019; Zbl 1477.65110) Full Text: DOI
Kalogiratou, Zacharoula; Monovasilis, Theodore; Simos, Theodore E. New fifth-order two-derivative Runge-Kutta methods with constant and frequency-dependent coefficients. (English) Zbl 1416.65194 Math. Methods Appl. Sci. 42, No. 6, 1955-1966 (2019). MSC: 65L05 PDFBibTeX XMLCite \textit{Z. Kalogiratou} et al., Math. Methods Appl. Sci. 42, No. 6, 1955--1966 (2019; Zbl 1416.65194) Full Text: DOI
D’Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems. (English) Zbl 1498.65187 Comput. Phys. Commun. 226, 55-66 (2018). MSC: 65N06 35K57 PDFBibTeX XMLCite \textit{R. D'Ambrosio} et al., Comput. Phys. Commun. 226, 55--66 (2018; Zbl 1498.65187) Full Text: DOI
Li, Jiyong; Deng, Shuo Trigonometrically fitted multi-step RKN methods for second-order oscillatory initial value problems. (English) Zbl 1426.65100 Appl. Math. Comput. 320, 740-753 (2018). MSC: 65L06 34C10 PDFBibTeX XMLCite \textit{J. Li} and \textit{S. Deng}, Appl. Math. Comput. 320, 740--753 (2018; Zbl 1426.65100) Full Text: DOI
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. Trigonometrical fitting conditions for two derivative Runge-Kutta methods. (English) Zbl 1416.65207 Numer. Algorithms 79, No. 3, 787-800 (2018). MSC: 65L06 65L05 65L20 PDFBibTeX XMLCite \textit{Th. Monovasilis} et al., Numer. Algorithms 79, No. 3, 787--800 (2018; Zbl 1416.65207) Full Text: DOI
Li, Jiyong; Wang, Xianfen; Deng, Shuo; Wang, Bin Symmetric trigonometrically-fitted two-step hybrid methods for oscillatory problems. (English) Zbl 1460.65090 J. Comput. Appl. Math. 344, 115-131 (2018). MSC: 65L06 65L05 65L20 PDFBibTeX XMLCite \textit{J. Li} et al., J. Comput. Appl. Math. 344, 115--131 (2018; Zbl 1460.65090) Full Text: DOI
Ehigie, Julius O.; Zou, Manman; Hou, Xilin; You, Xiong On modified TDRKN methods for second-order systems of differential equations. (English) Zbl 1390.65050 Int. J. Comput. Math. 95, No. 1, 159-173 (2018). MSC: 65L05 65L06 65L12 65L20 PDFBibTeX XMLCite \textit{J. O. Ehigie} et al., Int. J. Comput. Math. 95, No. 1, 159--173 (2018; Zbl 1390.65050) Full Text: DOI
D’Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice Adapted numerical methods for advection-reaction-diffusion problems generating periodic wavefronts. (English) Zbl 1448.65135 Comput. Math. Appl. 74, No. 5, 1029-1042 (2017). MSC: 65M20 65M06 65L05 35K51 65M50 35B45 PDFBibTeX XMLCite \textit{R. D'Ambrosio} et al., Comput. Math. Appl. 74, No. 5, 1029--1042 (2017; Zbl 1448.65135) Full Text: DOI
Chen, Zhaoxia; Zhang, Ruqiang; Shi, Wei; You, Xiong New optimized symmetric and symplectic trigonometrically fitted RKN methods for second-order oscillatory differential equations. (English) Zbl 1373.65047 Int. J. Comput. Math. 94, No. 5, 1036-1061 (2017). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 65L06 65L05 65L12 65P10 37M15 34C10 PDFBibTeX XMLCite \textit{Z. Chen} et al., Int. J. Comput. Math. 94, No. 5, 1036--1061 (2017; Zbl 1373.65047) Full Text: DOI
Monovasilis, T.; Kalogiratou, Z.; Simos, T. E. Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods. (English) Zbl 1347.65123 Mediterr. J. Math. 13, No. 4, 2271-2285 (2016). MSC: 65L06 65L05 65P10 37M15 34A34 PDFBibTeX XMLCite \textit{T. Monovasilis} et al., Mediterr. J. Math. 13, No. 4, 2271--2285 (2016; Zbl 1347.65123) Full Text: DOI
Franco, J. M.; Gómez, I. Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs. (English) Zbl 1410.65261 Appl. Math. Comput. 232, 643-657 (2014). MSC: 65L06 65L05 34A34 34C15 PDFBibTeX XMLCite \textit{J. M. Franco} and \textit{I. Gómez}, Appl. Math. Comput. 232, 643--657 (2014; Zbl 1410.65261) Full Text: DOI
D’Ambrosio, R.; Ferro, M.; Paternoster, B. Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations. (English) Zbl 1210.65133 Math. Comput. Simul. 81, No. 5, 1068-1084 (2011). MSC: 65L06 65L05 34A34 65L20 34C10 34C25 PDFBibTeX XMLCite \textit{R. D'Ambrosio} et al., Math. Comput. Simul. 81, No. 5, 1068--1084 (2011; Zbl 1210.65133) Full Text: DOI
Fang, Yonglei; Wu, Xinyuan A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions. (English) Zbl 1136.65068 Appl. Numer. Math. 58, No. 3, 341-351 (2008). MSC: 65L06 65L05 34A34 65L20 34C25 34C10 PDFBibTeX XMLCite \textit{Y. Fang} and \textit{X. Wu}, Appl. Numer. Math. 58, No. 3, 341--351 (2008; Zbl 1136.65068) Full Text: DOI
Fang, Yonglei; Wu, Xinyuan A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems. (English) Zbl 1344.65060 Appl. Math. Comput. 189, No. 1, 178-185 (2007). MSC: 65L05 70-08 PDFBibTeX XMLCite \textit{Y. Fang} and \textit{X. Wu}, Appl. Math. Comput. 189, No. 1, 178--185 (2007; Zbl 1344.65060) Full Text: DOI
Anastassi, Z. A.; Simos, T. E. A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation. (English) Zbl 1125.81017 J. Math. Chem. 41, No. 1, 79-100 (2007). MSC: 81Q05 81-08 65L06 PDFBibTeX XMLCite \textit{Z. A. Anastassi} and \textit{T. E. Simos}, J. Math. Chem. 41, No. 1, 79--100 (2007; Zbl 1125.81017) Full Text: DOI
Psihoyios, G.; Simos, T. E. A new trigonometrically-fitted sixth algebraic order P-C algorithm for the numerical solution of the radial Schrödinger equation. (English) Zbl 1085.65060 Math. Comput. Modelling 42, No. 7-8, 887-902 (2005). MSC: 65L05 65L06 34A34 PDFBibTeX XMLCite \textit{G. Psihoyios} and \textit{T. E. Simos}, Math. Comput. Modelling 42, No. 7--8, 887--902 (2005; Zbl 1085.65060) Full Text: DOI
Anastassi, Z. A.; Simos, T. E. Trigonometrically fitted fifth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation. (English) Zbl 1085.65063 Math. Comput. Modelling 42, No. 7-8, 877-886 (2005). MSC: 65L10 34B05 65L06 65L70 PDFBibTeX XMLCite \textit{Z. A. Anastassi} and \textit{T. E. Simos}, Math. Comput. Modelling 42, No. 7--8, 877--886 (2005; Zbl 1085.65063) Full Text: DOI
Anastassi, Z. A.; Simos, T. E. Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation. (English) Zbl 1070.81035 J. Math. Chem. 37, No. 3, 281-293 (2005). MSC: 81Q05 81-08 65L06 PDFBibTeX XMLCite \textit{Z. A. Anastassi} and \textit{T. E. Simos}, J. Math. Chem. 37, No. 3, 281--293 (2005; Zbl 1070.81035) Full Text: DOI
Simos, T. E. Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution. (English) Zbl 1062.65075 Appl. Math. Lett. 17, No. 5, 601-607 (2004). MSC: 65L06 65L05 34A34 PDFBibTeX XMLCite \textit{T. E. Simos}, Appl. Math. Lett. 17, No. 5, 601--607 (2004; Zbl 1062.65075) Full Text: DOI
Psihoyios, G.; Simos, T. E. Exponentially and trigonometrically fitted explicit advanced step-point (EAS) methods for initial value problems with oscillating solutions. (English) Zbl 1079.34549 Int. J. Mod. Phys. C 14, No. 2, 175-184 (2003). MSC: 34K28 PDFBibTeX XMLCite \textit{G. Psihoyios} and \textit{T. E. Simos}, Int. J. Mod. Phys. C 14, No. 2, 175--184 (2003; Zbl 1079.34549) Full Text: DOI
Simos, T. E.; Williams, P. S. Exponentially-fitted Runge-Kutta third algebraic order methods for the numerical solution of the Schrödinger equation and related problems. (English) Zbl 0945.65076 Int. J. Mod. Phys. C 10, No. 5, 839-851 (1999). MSC: 65L06 65L05 34L40 PDFBibTeX XMLCite \textit{T. E. Simos} and \textit{P. S. Williams}, Int. J. Mod. Phys. C 10, No. 5, 839--851 (1999; Zbl 0945.65076) Full Text: DOI