Khasi, Manoochehr; Rashidinia, Jalil; Rasoulizadeh, Mohammad Navaz Fast computing approaches based on a bilinear pseudo-spectral method for nonlinear acoustic wave equations. (English) Zbl 07710280 SIAM J. Sci. Comput. 45, No. 4, B413-B439 (2023). MSC: 65M70 65L06 65F15 65N15 35L05 41A60 76Q05 35Q35 15A18 PDF BibTeX XML Cite \textit{M. Khasi} et al., SIAM J. Sci. Comput. 45, No. 4, B413--B439 (2023; Zbl 07710280) Full Text: DOI
Zhang, Chengjian; Wang, Siyi; Tang, Changyang Error analysis of modified Runge-Kutta-Nyström methods for nonlinear second-order delay boundary value problems. (English) Zbl 07708821 Appl. Math. Lett. 142, Article ID 108658, 7 p. (2023). MSC: 65L10 65L06 PDF BibTeX XML Cite \textit{C. Zhang} et al., Appl. Math. Lett. 142, Article ID 108658, 7 p. (2023; Zbl 07708821) Full Text: DOI
Demba, Musa Ahmed; Senu, Norazak; Ramos, Higinio; Kumam, Poom; Watthayu, Wiboonsak A phase- and amplification-fitted 5(4) diagonally implicit Runge-Kutta-Nyström pair for oscillatory systems. (English) Zbl 1514.65089 Bull. Iran. Math. Soc. 49, No. 3, Paper No. 24, 23 p. (2023). MSC: 65L06 65L05 65L20 PDF BibTeX XML Cite \textit{M. A. Demba} et al., Bull. Iran. Math. Soc. 49, No. 3, Paper No. 24, 23 p. (2023; Zbl 1514.65089) Full Text: DOI
Liu, Changying; Li, Jiayin; Yang, Zhenqi; Tang, Yumeng; Liu, Kai Two high-order energy-preserving and symmetric Gauss collocation integrators for solving the hyperbolic Hamiltonian systems. (English) Zbl 07627985 Math. Comput. Simul. 205, 19-32 (2023). MSC: 65-XX 37-XX PDF BibTeX XML Cite \textit{C. Liu} et al., Math. Comput. Simul. 205, 19--32 (2023; Zbl 07627985) Full Text: DOI
Abdulsalam, Athraa; Senu, Norazak; Majid, Zanariah Abdul; Nik Long, Nik Mohd Asri Adaptive multi-step Runge-Kutta-Nyström methods for general second-order ordinary differential equations. (English) Zbl 1506.65100 J. Comput. Appl. Math. 421, Article ID 114874, 24 p. (2023). MSC: 65L06 PDF BibTeX XML Cite \textit{A. Abdulsalam} et al., J. Comput. Appl. Math. 421, Article ID 114874, 24 p. (2023; Zbl 1506.65100) Full Text: DOI
Kovalnogov, V. N.; Fedorov, R. V.; Karpukhina, M. T.; Kornilova, M. I.; Simos, T. E.; Tsitouras, Ch. Runge-Kutta-Nyström methods of eighth order for addressing linear inhomogeneous problems. (English) Zbl 1496.65088 J. Comput. Appl. Math. 419, Article ID 114778, 12 p. (2023). MSC: 65L06 65L05 PDF BibTeX XML Cite \textit{V. N. Kovalnogov} et al., J. Comput. Appl. Math. 419, Article ID 114778, 12 p. (2023; Zbl 1496.65088) Full Text: DOI
Blanes, S.; Casas, F.; Escorihuela-Tomàs, A. Runge-Kutta-Nyström symplectic splitting methods of order 8. (English) Zbl 1506.65102 Appl. Numer. Math. 182, 14-27 (2022). MSC: 65L06 65P10 PDF BibTeX XML Cite \textit{S. Blanes} et al., Appl. Numer. Math. 182, 14--27 (2022; Zbl 1506.65102) Full Text: DOI arXiv
Muthukumar, T.; Jayakumar, T.; Bharathi, D. Prasantha Numerical solution of fuzzy neutral delay differential equations by fifth order Runge-Kutta Nystrom method. (English) Zbl 1507.65113 J. Appl. Nonlinear Dyn. 11, No. 3, 703-717 (2022). MSC: 65L03 34K36 34K40 65L06 PDF BibTeX XML Cite \textit{T. Muthukumar} et al., J. Appl. Nonlinear Dyn. 11, No. 3, 703--717 (2022; Zbl 1507.65113) Full Text: DOI
Zhai, Wenjuan; Fu, Shuhuan; Zhou, Tianchong; Xiu, Chun Exponentially-fitted and trigonometrically-fitted implicit RKN methods for solving \(y^{\prime\prime}=f(t,y)\). (English) Zbl 1490.65140 J. Appl. Math. Comput. 68, No. 2, 1449-1466 (2022). MSC: 65L05 65L06 65M20 65N40 PDF BibTeX XML Cite \textit{W. Zhai} et al., J. Appl. Math. Comput. 68, No. 2, 1449--1466 (2022; Zbl 1490.65140) Full Text: DOI
Chen, Bingzhen; Zhai, Wenjuan Optimal three-stage implicit exponentially-fitted RKN methods for solving second-order ODEs. (English) Zbl 1492.65203 Calcolo 59, No. 1, Paper No. 14, 18 p. (2022). MSC: 65L06 65L05 PDF BibTeX XML Cite \textit{B. Chen} and \textit{W. Zhai}, Calcolo 59, No. 1, Paper No. 14, 18 p. (2022; Zbl 1492.65203) Full Text: DOI
Simos, T. E.; Tsitouras, Ch. On high order Runge-Kutta-Nyström pairs. (English) Zbl 1482.65110 J. Comput. Appl. Math. 400, Article ID 113753, 10 p. (2022). MSC: 65L05 65L06 PDF BibTeX XML Cite \textit{T. E. Simos} and \textit{Ch. Tsitouras}, J. Comput. Appl. Math. 400, Article ID 113753, 10 p. (2022; Zbl 1482.65110) Full Text: DOI
Hoang, N. S. Collocation Runge-Kutta-Nyström methods for solving second-order initial value problems. (English) Zbl 1480.65167 Int. J. Comput. Math. 98, No. 12, 2423-2444 (2021). MSC: 65L05 65L06 65L20 65L60 PDF BibTeX XML Cite \textit{N. S. Hoang}, Int. J. Comput. Math. 98, No. 12, 2423--2444 (2021; Zbl 1480.65167) Full Text: DOI
Daneshyar, Alireza; Sotoudeh, Payam; Ghaemian, Mohsen A shooting approach to the scaled boundary finite element equations of elastodynamics in the frequency domain. (English) Zbl 1507.74463 Comput. Methods Appl. Mech. Eng. 387, Article ID 114170, 27 p. (2021). MSC: 74S05 65M60 74B05 74D05 PDF BibTeX XML Cite \textit{A. Daneshyar} et al., Comput. Methods Appl. Mech. Eng. 387, Article ID 114170, 27 p. (2021; Zbl 1507.74463) Full Text: DOI
Liu, Kai; Fu, Ting; Shi, Wei Stability analysis for explicit ERKN methods solving general second-order oscillatory systems. (English) Zbl 07419038 Bull. Malays. Math. Sci. Soc. (2) 44, No. 6, 4143-4154 (2021). MSC: 65L05 65L06 PDF BibTeX XML Cite \textit{K. Liu} et al., Bull. Malays. Math. Sci. Soc. (2) 44, No. 6, 4143--4154 (2021; Zbl 07419038) Full Text: DOI
Daneshyar, Alireza; Ghaemian, Mohsen A general solution procedure for the scaled boundary finite element method via shooting technique. (English) Zbl 1507.74462 Comput. Methods Appl. Mech. Eng. 384, Article ID 113996, 22 p. (2021). MSC: 74S05 65L60 65L06 PDF BibTeX XML Cite \textit{A. Daneshyar} and \textit{M. Ghaemian}, Comput. Methods Appl. Mech. Eng. 384, Article ID 113996, 22 p. (2021; Zbl 1507.74462) Full Text: DOI
Sun, Xue; Liu, Zhongli; Tian, Hongjiong An alternative approach for order conditions of Runge-Kutta-Nyström methods. (English) Zbl 07400552 Adv. Comput. Math. 47, No. 5, Paper No. 70, 21 p. (2021). MSC: 65L05 65L06 PDF BibTeX XML Cite \textit{X. Sun} et al., Adv. Comput. Math. 47, No. 5, Paper No. 70, 21 p. (2021; Zbl 07400552) Full Text: DOI
Wu, Xinyuan; Wang, Bin; Mei, Lijie Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs. (English) Zbl 1459.65106 Numer. Algorithms 86, No. 2, 693-727 (2021). MSC: 65L05 65L06 65P10 PDF BibTeX XML Cite \textit{X. Wu} et al., Numer. Algorithms 86, No. 2, 693--727 (2021; Zbl 1459.65106) Full Text: DOI
Bujanda, B.; Moreta, M. J.; Jorge, J. C. New fractional step Runge-Kutta-Nyström methods up to order three. (English) Zbl 1433.65121 Appl. Math. Comput. 366, Article ID 124743, 19 p. (2020). MSC: 65L04 65L06 65L20 65L05 34A08 PDF BibTeX XML Cite \textit{B. Bujanda} et al., Appl. Math. Comput. 366, Article ID 124743, 19 p. (2020; Zbl 1433.65121) Full Text: DOI
Wang, Bin; Wu, Xinyuan Volume-preserving exponential integrators and their applications. (English) Zbl 1452.37083 J. Comput. Phys. 396, 867-887 (2019). MSC: 37M15 65L20 PDF BibTeX XML Cite \textit{B. Wang} and \textit{X. Wu}, J. Comput. Phys. 396, 867--887 (2019; Zbl 1452.37083) Full Text: DOI arXiv
You, Xiong; Zhang, Ruqiang; Huang, Ting; Fang, Yonglei Symmetric collocation ERKN methods for general second-order oscillators. (English) Zbl 1431.65103 Calcolo 56, No. 4, Paper No. 52, 22 p. (2019). MSC: 65L05 65L06 65L12 PDF BibTeX XML Cite \textit{X. You} et al., Calcolo 56, No. 4, Paper No. 52, 22 p. (2019; Zbl 1431.65103) Full Text: DOI
Amodio, Pierluigi; Brugnano, Luigi; Iavernaro, Felice A note on the continuous-stage Runge-Kutta(-Nyström) formulation of Hamiltonian boundary value methods (HBVMs). (English) Zbl 1433.65123 Appl. Math. Comput. 363, Article ID 124634, 8 p. (2019). MSC: 65L05 65P10 34A45 PDF BibTeX XML Cite \textit{P. Amodio} et al., Appl. Math. Comput. 363, Article ID 124634, 8 p. (2019; Zbl 1433.65123) Full Text: DOI arXiv
Tang, Wensheng; Sun, Yajuan; Zhang, Jingjing High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods. (English) Zbl 1429.65299 Appl. Math. Comput. 361, 670-679 (2019). MSC: 65P10 65L06 PDF BibTeX XML Cite \textit{W. Tang} et al., Appl. Math. Comput. 361, 670--679 (2019; Zbl 1429.65299) Full Text: DOI arXiv
Tang, Wensheng; Zhang, Jingjing Symmetric integrators based on continuous-stage Runge-Kutta-Nyström methods for reversible systems. (English) Zbl 1429.65155 Appl. Math. Comput. 361, 1-12 (2019). MSC: 65L06 65P10 PDF BibTeX XML Cite \textit{W. Tang} and \textit{J. Zhang}, Appl. Math. Comput. 361, 1--12 (2019; Zbl 1429.65155) Full Text: DOI arXiv
Zhao, Jingjun; Li, Yu; Xu, Yang An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations. (English) Zbl 1429.65209 Appl. Math. Comput. 351, 124-138 (2019). MSC: 65M06 35R11 65M12 PDF BibTeX XML Cite \textit{J. Zhao} et al., Appl. Math. Comput. 351, 124--138 (2019; Zbl 1429.65209) Full Text: DOI
Zhai, Wenjuan; Chen, Bingzhen A fourth order implicit symmetric and symplectic exponentially fitted Runge-Kutta-Nyström method for solving oscillatory problems. (English) Zbl 1422.65116 Numer. Algebra Control Optim. 9, No. 1, 71-84 (2019). MSC: 65L06 65L05 65M20 65N40 PDF BibTeX XML Cite \textit{W. Zhai} and \textit{B. Chen}, Numer. Algebra Control Optim. 9, No. 1, 71--84 (2019; Zbl 1422.65116) Full Text: DOI
Li, Jiyong; Wu, Xinyuan Energy-preserving continuous stage extended Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems. (English) Zbl 1448.65266 Appl. Numer. Math. 145, 469-487 (2019). MSC: 65P10 65L06 37M15 PDF BibTeX XML Cite \textit{J. Li} and \textit{X. Wu}, Appl. Numer. Math. 145, 469--487 (2019; Zbl 1448.65266) Full Text: DOI
Li, Jiyong; Gao, Yachao Energy-preserving trigonometrically fitted continuous stage Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems. (English) Zbl 1416.65514 Numer. Algorithms 81, No. 4, 1379-1401 (2019). MSC: 65P10 65L06 65L05 PDF BibTeX XML Cite \textit{J. Li} and \textit{Y. Gao}, Numer. Algorithms 81, No. 4, 1379--1401 (2019; Zbl 1416.65514) Full Text: DOI
Wang, Bin; Wu, Xinyuan Global error bounds of one-stage extended RKN integrators for semilinear wave equations. (English) Zbl 1422.65229 Numer. Algorithms 81, No. 4, 1203-1218 (2019). MSC: 65M15 65P10 65L70 PDF BibTeX XML Cite \textit{B. Wang} and \textit{X. Wu}, Numer. Algorithms 81, No. 4, 1203--1218 (2019; Zbl 1422.65229) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{Z. Chen} et al., Appl. Numer. Math. 142, 171--189 (2019; Zbl 1477.65110) Full Text: DOI
Li, Jiyong; Shi, Wei; Wu, Xinyuan The existence of explicit symplectic ARKN methods with several stages and algebraic order greater than two. (English) Zbl 1433.65340 J. Comput. Appl. Math. 353, 204-209 (2019). MSC: 65P10 65L06 37M15 PDF BibTeX XML Cite \textit{J. Li} et al., J. Comput. Appl. Math. 353, 204--209 (2019; Zbl 1433.65340) Full Text: DOI
Ma, Qiang; Song, Yuanwei; Xiao, Wei; Qin, Wendi; Ding, Xiaohua Structure-preserving stochastic Runge-Kutta-Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise. (English) Zbl 1459.65014 Adv. Difference Equ. 2019, Paper No. 192, 18 p. (2019). MSC: 65C30 60H10 60H35 34F05 65L06 37M15 65P10 PDF BibTeX XML Cite \textit{Q. Ma} et al., Adv. Difference Equ. 2019, Paper No. 192, 18 p. (2019; Zbl 1459.65014) Full Text: DOI
Li, Jiyong Symplectic and symmetric trigonometrically-fitted ARKN methods. (English) Zbl 1404.65311 Appl. Numer. Math. 135, 381-395 (2019). MSC: 65P10 65L06 34A34 65L05 PDF BibTeX XML Cite \textit{J. Li}, Appl. Numer. Math. 135, 381--395 (2019; Zbl 1404.65311) Full Text: DOI
Chen, Bing Zhen; Zhai, Wen Juan Implicit symmetric and symplectic exponentially fitted modified Runge-Kutta-Nyström methods for solving oscillatory problems. (English) Zbl 1498.65120 J. Inequal. Appl. 2018, Paper No. 321, 17 p. (2018). MSC: 65L06 65L05 34C10 34C15 PDF BibTeX XML Cite \textit{B. Z. Chen} and \textit{W. J. Zhai}, J. Inequal. Appl. 2018, Paper No. 321, 17 p. (2018; Zbl 1498.65120) Full Text: DOI
Tang, Wensheng; Zhang, Jingjing Symplecticity-preserving continuous-stage Runge-Kutta-Nyström methods. (English) Zbl 1426.65203 Appl. Math. Comput. 323, 204-219 (2018). MSC: 65P10 65L06 65L05 PDF BibTeX XML Cite \textit{W. Tang} and \textit{J. Zhang}, Appl. Math. Comput. 323, 204--219 (2018; Zbl 1426.65203) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{J. Li} and \textit{S. Deng}, Appl. Math. Comput. 320, 740--753 (2018; Zbl 1426.65100) Full Text: DOI
Nguyen-Ba, Truong; Giordano, Thierry; Vaillancourt, Rémi On Runge-Kutta-Nystrom formulae with contractivity preserving properties for second order ODEs. (English) Zbl 1424.65101 Acta Univ. Apulensis, Math. Inform. 54, 89-113 (2018). MSC: 65L06 PDF BibTeX XML Cite \textit{T. Nguyen-Ba} et al., Acta Univ. Apulensis, Math. Inform. 54, 89--113 (2018; Zbl 1424.65101) Full Text: DOI
Li, Jiyong; Deng, Shuo; Wang, Xianfen Extended explicit pseudo two-step RKN methods for oscillatory systems \(y^{\prime\prime} + My = f(y)\). (English) Zbl 1416.65206 Numer. Algorithms 78, No. 3, 673-700 (2018). MSC: 65L06 65L05 34A34 65L20 65L70 65Y05 PDF BibTeX XML Cite \textit{J. Li} et al., Numer. Algorithms 78, No. 3, 673--700 (2018; Zbl 1416.65206) Full Text: DOI
Zhao, Jingjun; Li, Yu; Xu, Yang Multiderivative extended Runge-Kutta-Nyström methods for multi-frequency oscillatory systems. (English) Zbl 1390.65055 Int. J. Comput. Math. 95, No. 1, 231-254 (2018). MSC: 65L20 PDF BibTeX XML Cite \textit{J. Zhao} et al., Int. J. Comput. Math. 95, No. 1, 231--254 (2018; Zbl 1390.65055) 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 PDF BibTeX XML Cite \textit{J. O. Ehigie} et al., Int. J. Comput. Math. 95, No. 1, 159--173 (2018; Zbl 1390.65050) Full Text: DOI
Wu, Xinyuan; Wang, Bin Recent developments in structure-preserving algorithms for oscillatory differential equations. (English) Zbl 1444.65003 Singapore: Springer; Beijing: Science Press (ISBN 978-981-10-9003-5/hbk; 978-981-10-9004-2/ebook). xv, 345 p. (2018). Reviewer: Piotr Biler (Wrocław) MSC: 65-02 65P10 65Lxx 65Nxx 65Mxx PDF BibTeX XML Cite \textit{X. Wu} and \textit{B. Wang}, Recent developments in structure-preserving algorithms for oscillatory differential equations. Singapore: Springer; Beijing: Science Press (2018; Zbl 1444.65003) Full Text: DOI
Liu, Kai; Wu, Xinyuan; Shi, Wei Extended phase properties and stability analysis of RKN-type integrators for solving general oscillatory second-order initial value problems. (English) Zbl 1381.65053 Numer. Algorithms 77, No. 1, 37-56 (2018). MSC: 65L05 65L06 65L20 34A34 34C10 PDF BibTeX XML Cite \textit{K. Liu} et al., Numer. Algorithms 77, No. 1, 37--56 (2018; Zbl 1381.65053) Full Text: DOI
Duruflé, Marc; N’diaye, Mamadou Optimized high order explicit Runge-Kutta-Nyström schemes. (English) Zbl 1382.65204 Bittencourt, Marco L. (ed.) et al., Spectral and high order methods for partial differential equations, ICOSAHOM 2016. Selected papers from the ICOSAHOM conference, June 27 – July 1, 2016, Rio de Janeiro, Brazil. Cham: Springer (ISBN 978-3-319-65869-8/hbk; 978-3-319-65870-4/ebook). Lecture Notes in Computational Science and Engineering 119, 599-612 (2017). MSC: 65L06 65L05 34A34 65L20 65L07 PDF BibTeX XML Cite \textit{M. Duruflé} and \textit{M. N'diaye}, Lect. Notes Comput. Sci. Eng. 119, 599--612 (2017; Zbl 1382.65204) Full Text: DOI HAL
Zeng, Xianyang; Yang, Hongli; Wu, Xinyuan An improved tri-coloured rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems. (English) Zbl 1376.65106 Numer. Algorithms 75, No. 4, 909-935 (2017). MSC: 65L06 65L05 34A34 94C10 PDF BibTeX XML Cite \textit{X. Zeng} et al., Numer. Algorithms 75, No. 4, 909--935 (2017; Zbl 1376.65106) Full Text: DOI
Luo, Yuesheng; Li, Xiaole; Guo, Cui Fourth-order compact and energy conservative scheme for solving nonlinear Klein-Gordon equation. (English) Zbl 1377.65119 Numer. Methods Partial Differ. Equations 33, No. 4, 1283-1304 (2017). Reviewer: Costică Moroşanu (Iaşi) MSC: 65M20 35Q40 65L06 65M12 65M06 PDF BibTeX XML Cite \textit{Y. Luo} et al., Numer. Methods Partial Differ. Equations 33, No. 4, 1283--1304 (2017; Zbl 1377.65119) 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 PDF BibTeX XML Cite \textit{Z. Chen} et al., Int. J. Comput. Math. 94, No. 5, 1036--1061 (2017; Zbl 1373.65047) Full Text: DOI
Wang, Bin; Yang, Hongli; Meng, Fanwei Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations. (English) Zbl 1369.65169 Calcolo 54, No. 1, 117-140 (2017). MSC: 65P10 37M15 37J10 65L06 34C15 PDF BibTeX XML Cite \textit{B. Wang} et al., Calcolo 54, No. 1, 117--140 (2017; Zbl 1369.65169) Full Text: DOI
Wang, Bin; Meng, Fanwei; Fang, Yonglei Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations. (English) Zbl 1368.65114 Appl. Numer. Math. 119, 164-178 (2017). MSC: 65L06 65L05 34A34 65L60 PDF BibTeX XML Cite \textit{B. Wang} et al., Appl. Numer. Math. 119, 164--178 (2017; Zbl 1368.65114) Full Text: DOI arXiv
Casas, Fernando; Crouseilles, Nicolas; Faou, Erwan; Mehrenberger, Michel High-order Hamiltonian splitting for the Vlasov-Poisson equations. (English) Zbl 1369.37083 Numer. Math. 135, No. 3, 769-801 (2017). Reviewer: Kai Schneider (Marseille) MSC: 37M15 65M25 65M12 65P10 65Z05 82D10 37K05 PDF BibTeX XML Cite \textit{F. Casas} et al., Numer. Math. 135, No. 3, 769--801 (2017; Zbl 1369.37083) Full Text: DOI arXiv
Yang, Yanping; You, Xiong; Fang, Yonglei Runge-Kutta-Nyström methods with equation dependent coefficients and reduced phase lag for oscillatory problems. (English) Zbl 1359.65119 J. Math. Chem. 55, No. 1, 259-277 (2017). MSC: 65L06 65L05 34A34 34C10 65L20 PDF BibTeX XML Cite \textit{Y. Yang} et al., J. Math. Chem. 55, No. 1, 259--277 (2017; Zbl 1359.65119) Full Text: DOI
Li, Jiyong; Wang, Xianfen Multi-step Runge-Kutta-Nyström methods for special second-order initial value problems. (English) Zbl 1355.65097 Appl. Numer. Math. 113, 54-70 (2017). MSC: 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{J. Li} and \textit{X. Wang}, Appl. Numer. Math. 113, 54--70 (2017; Zbl 1355.65097) Full Text: DOI
Moreta, M. J.; Bujanda, Blanca; Jorge, J. C. Avoiding the order reduction when solving second-order in time PDEs with fractional step Runge-Kutta-Nyström methods. (English) Zbl 1443.65173 Comput. Math. Appl. 71, No. 7, 1425-1447 (2016). MSC: 65M20 65L06 65M06 65M60 35R11 PDF BibTeX XML Cite \textit{M. J. Moreta} et al., Comput. Math. Appl. 71, No. 7, 1425--1447 (2016; Zbl 1443.65173) Full Text: DOI
Salih, M.; Ismail, F.; Senu, N. Fifth order Runge-Kutta-Nyström methods for solving linear second order oscillatory problems. (English) Zbl 1359.65118 Far East J. Appl. Math. 95, No. 2, 141-156 (2016). MSC: 65L06 65L05 34A30 65L70 PDF BibTeX XML Cite \textit{M. Salih} et al., Far East J. Appl. Math. 95, No. 2, 141--156 (2016; Zbl 1359.65118) 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 PDF BibTeX XML Cite \textit{T. Monovasilis} et al., Mediterr. J. Math. 13, No. 4, 2271--2285 (2016; Zbl 1347.65123) Full Text: DOI
Bai, Jiejing Multi-symplectic Runge-Kutta-Nyström methods for nonsmooth nonlinear Schrödinger equations. (English) Zbl 1345.65065 J. Math. Anal. Appl. 444, No. 1, 721-736 (2016). MSC: 65P10 37M15 37K05 35Q55 35L65 65L06 PDF BibTeX XML Cite \textit{J. Bai}, J. Math. Anal. Appl. 444, No. 1, 721--736 (2016; Zbl 1345.65065) Full Text: DOI
Hoang, N. S.; Sidje, Roger B. Functionally fitted Runge-Kutta-Nyström methods. (English) Zbl 1359.65114 BIT 56, No. 1, 129-150 (2016). Reviewer: Maria Gousidou-Koutita (Thessaloniki) MSC: 65L06 65L05 65L20 65L60 34A34 PDF BibTeX XML Cite \textit{N. S. Hoang} and \textit{R. B. Sidje}, BIT 56, No. 1, 129--150 (2016; Zbl 1359.65114) Full Text: DOI arXiv
Wang, Bin; Iserles, Arieh; Wu, Xinyuan Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems. (English) Zbl 1341.65029 Found. Comput. Math. 16, No. 1, 151-181 (2016). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L60 65L05 65L20 65P10 37M15 34C10 34A34 65L06 PDF BibTeX XML Cite \textit{B. Wang} et al., Found. Comput. Math. 16, No. 1, 151--181 (2016; Zbl 1341.65029) Full Text: DOI
Mulloth, Akhil; Sawant, Nilesh; Haider, Ijlal; Sharma, Nidhi; Sengupta, Tapan K. High accuracy solution of bi-directional wave propagation in continuum mechanics. (English) Zbl 1349.76513 J. Comput. Phys. 298, 209-236 (2015). MSC: 76M20 65M06 35L10 65M12 76B15 PDF BibTeX XML Cite \textit{A. Mulloth} et al., J. Comput. Phys. 298, 209--236 (2015; Zbl 1349.76513) Full Text: DOI
Wu, Xinyuan; Liu, Kai; Shi, Wei Structure-preserving algorithms for oscillatory differential equations II. (English) Zbl 1352.65187 Berlin: Springer; Beijing: Science Press (ISBN 978-3-662-48155-4/hbk; 978-3-662-48156-1/ebook). xv, 298 p. (2015). Reviewer: Roland Pulch (Greifswald) MSC: 65L05 65-02 65L06 65L70 65P10 34C10 37M15 37J05 PDF BibTeX XML Cite \textit{X. Wu} et al., Structure-preserving algorithms for oscillatory differential equations II. Berlin: Springer; Beijing: Science Press (2015; Zbl 1352.65187) Full Text: DOI
Chen, Zhaoxia; Qiu, Zeyu; Li, Juan; You, Xiong Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations. (English) Zbl 1335.65059 Numer. Algorithms 70, No. 4, 897-927 (2015). Reviewer: Martin Reißel (Aachen) MSC: 65L06 65L05 34A34 65L20 PDF BibTeX XML Cite \textit{Z. Chen} et al., Numer. Algorithms 70, No. 4, 897--927 (2015; Zbl 1335.65059) Full Text: DOI
Liu, Kai; Wu, Xinyuan High-order symplectic and symmetric composition methods for multi-frequency and multi-dimensional oscillatory Hamiltonian systems. (English) Zbl 1340.65307 J. Comput. Math. 33, No. 4, 356-378 (2015). MSC: 65P10 65L06 37M15 PDF BibTeX XML Cite \textit{K. Liu} and \textit{X. Wu}, J. Comput. Math. 33, No. 4, 356--378 (2015; Zbl 1340.65307) Full Text: DOI
Kosti, Athinoula A.; Anastassi, Zacharias A. Explicit almost P-stable Runge-Kutta-Nyström methods for the numerical solution of the two-body problem. (English) Zbl 1321.65116 Comput. Appl. Math. 34, No. 2, 647-659 (2015). MSC: 65L06 65L05 34A34 70F05 65L20 65L70 PDF BibTeX XML Cite \textit{A. A. Kosti} and \textit{Z. A. Anastassi}, Comput. Appl. Math. 34, No. 2, 647--659 (2015; Zbl 1321.65116) Full Text: DOI
Cong, Nguyen Huu; Dung, La Tri Two-step-by-two-step PIRKN-type PC methods based on Gauss-Legendre collocation points for nonstiff IVPs. (English) Zbl 1315.65066 Comput. Appl. Math. 34, No. 1, 93-108 (2015). Reviewer: Yajuan Sun (Beijing) MSC: 65L06 65L05 65L20 65L60 34A34 65Y05 PDF BibTeX XML Cite \textit{N. H. Cong} and \textit{L. T. Dung}, Comput. Appl. Math. 34, No. 1, 93--108 (2015; Zbl 1315.65066) Full Text: DOI
Anastassi, Z. A.; Kosti, A. A. A 6(4) optimized embedded Runge-Kutta-Nyström pair for the numerical solution of periodic problems. (English) Zbl 1337.65066 J. Comput. Appl. Math. 275, 311-320 (2015). MSC: 65L05 65L06 PDF BibTeX XML Cite \textit{Z. A. Anastassi} and \textit{A. A. Kosti}, J. Comput. Appl. Math. 275, 311--320 (2015; Zbl 1337.65066) Full Text: DOI
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E. A fourth order modified trigonometrically fitted symplectic Runge-Kutta-Nyström method. (English) Zbl 1360.65300 Comput. Phys. Commun. 185, No. 12, 3151-3155 (2014). MSC: 65P10 37M15 PDF BibTeX XML Cite \textit{Z. Kalogiratou} et al., Comput. Phys. Commun. 185, No. 12, 3151--3155 (2014; Zbl 1360.65300) Full Text: DOI
Liu, Kai; Wu, Xinyuan Multidimensional ARKN methods for general oscillatory second-order initial value problems. (English) Zbl 1352.65183 Comput. Phys. Commun. 185, No. 7, 1999-2007 (2014). MSC: 65L05 65L06 PDF BibTeX XML Cite \textit{K. Liu} and \textit{X. Wu}, Comput. Phys. Commun. 185, No. 7, 1999--2007 (2014; Zbl 1352.65183) Full Text: DOI
Liu, Changying; Shi, Wei; Wu, Xinyuan An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations. (English) Zbl 1339.65130 Appl. Math. Comput. 246, 696-710 (2014). MSC: 65M06 65M20 PDF BibTeX XML Cite \textit{C. Liu} et al., Appl. Math. Comput. 246, 696--710 (2014; Zbl 1339.65130) Full Text: DOI
D’Ambrosio, R.; Paternoster, B.; Santomauro, G. Revised exponentially fitted Runge-Kutta-Nyström methods. (English) Zbl 1311.65097 Appl. Math. Lett. 30, 56-60 (2014). MSC: 65L06 34C25 34C10 PDF BibTeX XML Cite \textit{R. D'Ambrosio} et al., Appl. Math. Lett. 30, 56--60 (2014; Zbl 1311.65097) Full Text: DOI
Imoni, S. O.; Ikhile, M. N. O. Zero dissipative DIRKN pairs of order 5(4) for solving special second order IVPs. (English) Zbl 1311.65098 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 53, No. 2, 53-69 (2014). MSC: 65L06 65L05 34A34 34C10 PDF BibTeX XML Cite \textit{S. O. Imoni} and \textit{M. N. O. Ikhile}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 53, No. 2, 53--69 (2014; Zbl 1311.65098) Full Text: Link
Liu, Shiwei; Zheng, Juan; Fang, Yonglei A new embedded 5(3) pair of modified Runge-Kutta-Nyström methods for the numerical solution of the Schrödinger equation. (English) Zbl 1301.65073 J. Math. Chem. 52, No. 4, 1081-1098 (2014). MSC: 65L06 65L05 34A30 34L40 65L70 PDF BibTeX XML Cite \textit{S. Liu} et al., J. Math. Chem. 52, No. 4, 1081--1098 (2014; Zbl 1301.65073) Full Text: DOI
Franco, J. M.; Gómez, I. Symplectic explicit methods of Runge-Kutta-Nyström type for solving perturbed oscillators. (English) Zbl 1293.65102 J. Comput. Appl. Math. 260, 482-493 (2014). MSC: 65L06 65P10 PDF BibTeX XML Cite \textit{J. M. Franco} and \textit{I. Gómez}, J. Comput. Appl. Math. 260, 482--493 (2014; Zbl 1293.65102) Full Text: DOI
You, Xiong; Fang, Yonglei; Zhao, Jinxi Special extended Nyström tree theory for ERKN methods. (English) Zbl 1301.65076 J. Comput. Appl. Math. 263, 478-499 (2014). MSC: 65L06 65L05 65M20 PDF BibTeX XML Cite \textit{X. You} et al., J. Comput. Appl. Math. 263, 478--499 (2014; Zbl 1301.65076) Full Text: DOI
Wang, Bin; Wu, Xinyuan A highly accurate explicit symplectic ERKN method for multi-frequency and multidimensional oscillatory Hamiltonian systems. (English) Zbl 1291.65362 Numer. Algorithms 65, No. 3, 705-721 (2014). MSC: 65P10 37M15 65L06 PDF BibTeX XML Cite \textit{B. Wang} and \textit{X. Wu}, Numer. Algorithms 65, No. 3, 705--721 (2014; Zbl 1291.65362) Full Text: DOI
Li, Jiyong; Wu, Xinyuan Error analysis of explicit TSERKN methods for highly oscillatory systems. (English) Zbl 1293.65109 Numer. Algorithms 65, No. 3, 465-483 (2014). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65L70 65L06 65L05 65L20 34C10 PDF BibTeX XML Cite \textit{J. Li} and \textit{X. Wu}, Numer. Algorithms 65, No. 3, 465--483 (2014; Zbl 1293.65109) Full Text: DOI
You, Xiong; Zhao, Jinxi; Yang, Hongli; Fang, Yonglei; Wu, Xinyuan Order conditions for RKN methods solving general second-order oscillatory systems. (English) Zbl 1292.65083 Numer. Algorithms 66, No. 1, 147-176 (2014). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L06 65L05 34A34 34C10 PDF BibTeX XML Cite \textit{X. You} et al., Numer. Algorithms 66, No. 1, 147--176 (2014; Zbl 1292.65083) Full Text: DOI
You, Xiong; Chen, Bingzhen Symmetric and symplectic exponentially fitted Runge-Kutta-Nyström methods for Hamiltonian problems. (English) Zbl 1499.65728 Math. Comput. Simul. 94, 76-95 (2013). MSC: 65P10 65L05 65L06 PDF BibTeX XML Cite \textit{X. You} and \textit{B. Chen}, Math. Comput. Simul. 94, 76--95 (2013; Zbl 1499.65728) Full Text: DOI
Wu, Xinyuan; Wang, Bin; Liu, Kai; Zhao, Hua ERKN methods for long-term integration of multidimensional orbital problems. (English) Zbl 1349.65233 Appl. Math. Modelling 37, No. 4, 2327-2336 (2013). MSC: 65L06 70M20 34C15 37N05 37M10 PDF BibTeX XML Cite \textit{X. Wu} et al., Appl. Math. Modelling 37, No. 4, 2327--2336 (2013; Zbl 1349.65233) Full Text: DOI
Franco, J. M.; Gómez, I. Construction of explicit symmetric and symplectic methods of Runge-Kutta-Nyström type for solving perturbed oscillators. (English) Zbl 06447270 Appl. Math. Comput. 219, No. 9, 4637-4649 (2013). MSC: 65-XX 34-XX PDF BibTeX XML Cite \textit{J. M. Franco} and \textit{I. Gómez}, Appl. Math. Comput. 219, No. 9, 4637--4649 (2013; Zbl 06447270) Full Text: DOI
Franco, J. M.; Gómez, I. Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type. (English) Zbl 1301.65071 Comput. Phys. Commun. 184, No. 4, 1310-1321 (2013). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L06 65L05 65Y05 65L20 65L50 34C10 34A34 PDF BibTeX XML Cite \textit{J. M. Franco} and \textit{I. Gómez}, Comput. Phys. Commun. 184, No. 4, 1310--1321 (2013; Zbl 1301.65071) Full Text: DOI
Zhai, Wenjuan; Chen, Bingzhen Exponentially fitted RKNd methods for solving oscillatory ODEs. (English) Zbl 1299.65145 Adv. Math., Beijing 42, No. 3, 393-404 (2013). MSC: 65L06 65L05 65L20 34A34 PDF BibTeX XML Cite \textit{W. Zhai} and \textit{B. Chen}, Adv. Math., Beijing 42, No. 3, 393--404 (2013; Zbl 1299.65145)
Wang, Dongling; Zhu, Gang; Xiao, Aiguo R-stability and phase-lag of mono-implicit Runge-Kutta-Nyström methods for second order stiff differential equations. (Chinese. English summary) Zbl 1299.65163 Numer. Math., Nanjing 35, No. 2, 159-173 (2013). MSC: 65L20 65L04 65L05 65L06 34A34 PDF BibTeX XML Cite \textit{D. Wang} et al., Numer. Math., Nanjing 35, No. 2, 159--173 (2013; Zbl 1299.65163)
Papadopoulos, D. F.; Simos, T. E. The use of phase lag and amplification error derivatives for the construction of a modified Runge-Kutta-Nyström method. (English) Zbl 1275.65044 Abstr. Appl. Anal. 2013, Article ID 910624, 11 p. (2013). MSC: 65L06 65L05 34A34 65L70 34L40 PDF BibTeX XML Cite \textit{D. F. Papadopoulos} and \textit{T. E. Simos}, Abstr. Appl. Anal. 2013, Article ID 910624, 11 p. (2013; Zbl 1275.65044) Full Text: DOI
Ahmad, S. Z.; Ismail, F.; Senu, N.; Suleiman, M. Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems. (English) Zbl 1275.65042 Abstr. Appl. Anal. 2013, Article ID 136961, 10 p. (2013). MSC: 65L06 65L05 34A34 65L20 34C10 PDF BibTeX XML Cite \textit{S. Z. Ahmad} et al., Abstr. Appl. Anal. 2013, Article ID 136961, 10 p. (2013; Zbl 1275.65042) Full Text: DOI
Fang, Yonglei; You, Xiong; Ming, Qinghe New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation. (English) Zbl 1447.81109 J. Math. Chem. 51, No. 1, 390-411 (2013). MSC: 81Q05 65L06 37L05 PDF BibTeX XML Cite \textit{Y. Fang} et al., J. Math. Chem. 51, No. 1, 390--411 (2013; Zbl 1447.81109) Full Text: DOI
Sharp, Philip W.; Qureshi, Mohammad A.; Grazier, Kevin R. High order explicit Runge-Kutta Nyström pairs. (English) Zbl 1259.65120 Numer. Algorithms 62, No. 1, 133-148 (2013). MSC: 65L06 65L05 34A34 PDF BibTeX XML Cite \textit{P. W. Sharp} et al., Numer. Algorithms 62, No. 1, 133--148 (2013; Zbl 1259.65120) Full Text: DOI
Wu, Xinyuan; You, Xiong; Wang, Bin Structure-preserving algorithms for oscillatory differential equations. (English) Zbl 1276.65041 Berlin: Springer; Beijing: Science Press (ISBN 978-3-642-35337-6/hbk; 978-3-642-35338-3/ebook). xii, 236 p. (2013). Reviewer: Roland Pulch (Greifswald) MSC: 65L05 65-02 65L06 65P10 34A34 34C10 37M15 37J05 PDF BibTeX XML Cite \textit{X. Wu} et al., Structure-preserving algorithms for oscillatory differential equations. Berlin: Springer; Beijing: Science Press (2013; Zbl 1276.65041) Full Text: DOI
Wu, Xinyuan A note on stability of multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems. (English) Zbl 1349.65232 Appl. Math. Modelling 36, No. 12, 6331-6337 (2012). MSC: 65L06 65L20 34C15 PDF BibTeX XML Cite \textit{X. Wu}, Appl. Math. Modelling 36, No. 12, 6331--6337 (2012; Zbl 1349.65232) Full Text: DOI
Senu, Norazak; Suleiman, Mohamed; Ismail, Fudziah; Othman, Mohamed Analysis of phase-lag for diagonally implicit Runge-Kutta-Nyström methods. (English) Zbl 1308.65121 J. Appl. Math. Bioinform. 2, No. 2, 51-63 (2012). MSC: 65L06 65L05 34A30 34C10 PDF BibTeX XML Cite \textit{N. Senu} et al., J. Appl. Math. Bioinform. 2, No. 2, 51--63 (2012; Zbl 1308.65121)
Liu, Yuhua; Zhang, Jinliang; Li, Liutao The numerical simulation of the solutions for the generalized Burgers-Huxley equation. (Chinese. English summary) Zbl 1289.65184 J. Nanyang Norm. Univ. 11, No. 12, 6-10 (2012). MSC: 65M06 35Q53 PDF BibTeX XML Cite \textit{Y. Liu} et al., J. Nanyang Norm. Univ. 11, No. 12, 6--10 (2012; Zbl 1289.65184)
Guo, Changyong Stability of Runge-Kutta-Nyström method for a class of second order delay differential equations. (Chinese. English summary) Zbl 1274.65216 J. Nat. Sci. Heilongjiang Univ. 29, No. 3, 327-331 (2012). MSC: 65L20 65L06 65L07 34K28 34K20 PDF BibTeX XML Cite \textit{C. Guo}, J. Nat. Sci. Heilongjiang Univ. 29, No. 3, 327--331 (2012; Zbl 1274.65216)
Kosti, A. A.; Anastassi, Z. A.; Simos, T. E. An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems. (English) Zbl 1264.65111 Comput. Phys. Commun. 183, No. 3, 470-479 (2012). MSC: 65L06 65L05 34A34 65L70 70F05 PDF BibTeX XML Cite \textit{A. A. Kosti} et al., Comput. Phys. Commun. 183, No. 3, 470--479 (2012; Zbl 1264.65111) Full Text: DOI
Shi, Wei; Wu, Xinyuan On symplectic and symmetric ARKN methods. (English) Zbl 1356.65243 Comput. Phys. Commun. 183, No. 6, 1250-1258 (2012). MSC: 65P10 65L06 PDF BibTeX XML Cite \textit{W. Shi} and \textit{X. Wu}, Comput. Phys. Commun. 183, No. 6, 1250--1258 (2012; Zbl 1356.65243) Full Text: DOI
Chen, Zhaoxia; You, Xiong; Shi, Wei; Liu, Zhongli Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems. (English) Zbl 1266.65201 Comput. Phys. Commun. 183, No. 1, 86-98 (2012). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65P10 37M15 65L06 PDF BibTeX XML Cite \textit{Z. Chen} et al., Comput. Phys. Commun. 183, No. 1, 86--98 (2012; Zbl 1266.65201) Full Text: DOI
Wu, Xinyuan; Wang, Bin; Xia, Jianlin Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods. (English) Zbl 1258.65068 BIT 52, No. 3, 773-795 (2012). Reviewer: Romulus Militaru (Craiova) MSC: 65L06 65L05 34A34 65P10 37M15 34C10 PDF BibTeX XML Cite \textit{X. Wu} et al., BIT 52, No. 3, 773--795 (2012; Zbl 1258.65068) Full Text: DOI
Bujanda, B.; Jorge, J. C.; Moreta, M. J. Numerical resolution of linear evolution multidimensional problems of second order in time. (English) Zbl 1255.65101 Numer. Methods Partial Differ. Equations 28, No. 2, 597-620 (2012). Reviewer: Roland Pulch (Wuppertal) MSC: 65J08 65M12 65M22 65L06 65J10 34G10 65L20 PDF BibTeX XML Cite \textit{B. Bujanda} et al., Numer. Methods Partial Differ. Equations 28, No. 2, 597--620 (2012; Zbl 1255.65101) Full Text: DOI
Famelis, I. Th. Neural network-based derivation of efficient high-order Runge-Kutta-Nyström pairs for the integration of orbits. (English) Zbl 1263.65069 Int. J. Mod. Phys. C 22, No. 12, 1309-1316 (2011). MSC: 65L05 65L06 34A34 70M20 PDF BibTeX XML Cite \textit{I. Th. Famelis}, Int. J. Mod. Phys. C 22, No. 12, 1309--1316 (2011; Zbl 1263.65069) Full Text: DOI
Papadopoulos, D. F.; Simos, T. E. A new methodology for the construction of optimized Runge-Kutta-Nyström methods. (English) Zbl 1262.65080 Int. J. Mod. Phys. C 22, No. 6, 623-634 (2011). MSC: 65L06 65L05 34A34 34L40 65L70 PDF BibTeX XML Cite \textit{D. F. Papadopoulos} and \textit{T. E. Simos}, Int. J. Mod. Phys. C 22, No. 6, 623--634 (2011; Zbl 1262.65080) Full Text: DOI
Li, Jiyong; Wang, Bin; You, Xiong; Wu, Xinyuan Two-step extended RKN methods for oscillatory systems. (English) Zbl 1261.65078 Comput. Phys. Commun. 182, No. 12, 2486-2507 (2011). MSC: 65L06 65L05 34A34 34C15 PDF BibTeX XML Cite \textit{J. Li} et al., Comput. Phys. Commun. 182, No. 12, 2486--2507 (2011; Zbl 1261.65078) Full Text: DOI
Franco, J. M.; Gómez, I. A family of explicit parallel Runge-Kutta-Nyström methods. (English) Zbl 1319.65062 Appl. Math. Comput. 218, No. 8, 4177-4191 (2011). MSC: 65L06 65L05 65Y05 34A34 65L50 PDF BibTeX XML Cite \textit{J. M. Franco} and \textit{I. Gómez}, Appl. Math. Comput. 218, No. 8, 4177--4191 (2011; Zbl 1319.65062) Full Text: DOI
Senu, N.; Suleiman, M.; Ismail, F.; Othman, M. A singly diagonally implicit Runge-Kutta-Nyström method for solving oscillatory problems. (English) Zbl 1229.65124 IAENG, Int. J. Appl. Math. 41, No. 2, 155-161 (2011). MSC: 65L06 34C10 PDF BibTeX XML Cite \textit{N. Senu} et al., IAENG, Int. J. Appl. Math. 41, No. 2, 155--161 (2011; Zbl 1229.65124)
Chin, Siu A.; Geiser, Jürgen Multi-product operator splitting as a general method of solving autonomous and nonautonomous equations. (English) Zbl 1232.65174 IMA J. Numer. Anal. 31, No. 4, 1552-1577 (2011). Reviewer: Manuel Calvo (Zaragoza) MSC: 65P10 65L06 37M15 65L05 37C10 65L70 65L20 81Q05 PDF BibTeX XML Cite \textit{S. A. Chin} and \textit{J. Geiser}, IMA J. Numer. Anal. 31, No. 4, 1552--1577 (2011; Zbl 1232.65174) Full Text: DOI arXiv