Jiang, Chaolong; Cui, Jin; Qian, Xu; Song, Songhe High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation. (English) Zbl 1481.65134 J. Sci. Comput. 90, No. 1, Paper No. 66, 27 p. (2022). MSC: 65M06 65M70 65L06 35Q55 35Q41 PDFBibTeX XMLCite \textit{C. Jiang} et al., J. Sci. Comput. 90, No. 1, Paper No. 66, 27 p. (2022; Zbl 1481.65134) Full Text: DOI arXiv
Hu, Dongdong; Cai, Wenjun; Gu, Xian-Ming; Wang, Yushun Efficient energy preserving Galerkin-Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator. (English) Zbl 1484.65223 Appl. Numer. Math. 172, 608-628 (2022). MSC: 65M60 35Q55 35R11 65M12 65M15 PDFBibTeX XMLCite \textit{D. Hu} et al., Appl. Numer. Math. 172, 608--628 (2022; Zbl 1484.65223) Full Text: DOI
Frasca-Caccia, Gianluca; Hydon, Peter E. Numerical preservation of multiple local conservation laws. (English) Zbl 1510.65191 Appl. Math. Comput. 403, Article ID 126203, 23 p. (2021). MSC: 65M06 37K06 39A14 PDFBibTeX XMLCite \textit{G. Frasca-Caccia} and \textit{P. E. Hydon}, Appl. Math. Comput. 403, Article ID 126203, 23 p. (2021; Zbl 1510.65191) Full Text: DOI arXiv
Hu, Dongdong; Cai, Wenjun; Wang, Yushun Two linearly implicit energy preserving exponential scalar auxiliary variable approaches for multi-dimensional fractional nonlinear Schrödinger equations. (English) Zbl 1524.65351 Appl. Math. Lett. 122, Article ID 107544, 7 p. (2021). MSC: 65M06 35Q55 65M12 35R11 65P10 65N35 65B05 26A33 PDFBibTeX XMLCite \textit{D. Hu} et al., Appl. Math. Lett. 122, Article ID 107544, 7 p. (2021; Zbl 1524.65351) Full Text: DOI
Hu, Dongdong; Gong, Yuezheng; Wang, Yushun On convergence of a structure preserving difference scheme for two-dimensional space-fractional nonlinear Schrödinger equation and its fast implementation. (English) Zbl 1524.65352 Comput. Math. Appl. 98, 10-23 (2021). MSC: 65M06 35R11 35Q55 65M15 65M12 26A33 35Q41 65N06 15B05 65T50 65N20 65F08 65F10 PDFBibTeX XMLCite \textit{D. Hu} et al., Comput. Math. Appl. 98, 10--23 (2021; Zbl 1524.65352) Full Text: DOI
Akrivis, Georgios; Li, Dongfang Structure-preserving Gauss methods for the nonlinear Schrödinger equation. (English) Zbl 1486.65158 Calcolo 58, No. 2, Paper No. 17, 25 p. (2021). MSC: 65M60 65M06 65N30 65M12 35Q41 35Q55 PDFBibTeX XMLCite \textit{G. Akrivis} and \textit{D. Li}, Calcolo 58, No. 2, Paper No. 17, 25 p. (2021; Zbl 1486.65158) Full Text: DOI
Castillo, Paul; Gómez, Sergio Conservative super-convergent and hybrid discontinuous Galerkin methods applied to nonlinear Schrödinger equations. (English) Zbl 1433.65207 Appl. Math. Comput. 371, Article ID 124950, 14 p. (2020). MSC: 65M60 65M12 35Q55 PDFBibTeX XMLCite \textit{P. Castillo} and \textit{S. Gómez}, Appl. Math. Comput. 371, Article ID 124950, 14 p. (2020; Zbl 1433.65207) Full Text: DOI
Brugnano, Luigi; Zhang, Chengjian; Li, Dongfang A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator. (English) Zbl 1470.65205 Commun. Nonlinear Sci. Numer. Simul. 60, 33-49 (2018). MSC: 65P10 65M20 65M70 PDFBibTeX XMLCite \textit{L. Brugnano} et al., Commun. Nonlinear Sci. Numer. Simul. 60, 33--49 (2018; Zbl 1470.65205) Full Text: DOI Link
Barletti, L.; Brugnano, L.; Frasca Caccia, G.; Iavernaro, F. Energy-conserving methods for the nonlinear Schrödinger equation. (English) Zbl 1426.65202 Appl. Math. Comput. 318, 3-18 (2018). MSC: 65P10 35Q55 65L05 65M20 37M15 PDFBibTeX XMLCite \textit{L. Barletti} et al., Appl. Math. Comput. 318, 3--18 (2018; Zbl 1426.65202) Full Text: DOI Link