Pan, Kejia; Zeng, Jiali; He, Dongdong; Zhang, Saiyan A fourth-order difference scheme for the fractional nonlinear Schrödinger equation with wave operator. (English) Zbl 07548873 Appl. Anal. 101, No. 8, 2886-2902 (2022). MSC: 65M06 PDF BibTeX XML Cite \textit{K. Pan} et al., Appl. Anal. 101, No. 8, 2886--2902 (2022; Zbl 07548873) Full Text: DOI OpenURL
Besse, Christophe; Duboscq, Romain; Le Coz, Stefan Numerical simulations on nonlinear quantum graphs with the GraFiDi library. (English) Zbl 07525072 SMAI J. Comput. Math. 8, 1-47 (2022). MSC: 65-XX 35R02 65N06 35Q55 PDF BibTeX XML Cite \textit{C. Besse} et al., SMAI J. Comput. Math. 8, 1--47 (2022; Zbl 07525072) Full Text: DOI OpenURL
Besse, Christophe; Duboscq, Romain; Le Coz, Stefan Gradient flow approach to the calculation of stationary states on nonlinear quantum graphs. (Une approche flot gradient pour le calcul des états stationnaires sur des graphes quantiques non linéaires.) (English. French summary) Zbl 07524689 Ann. Henri Lebesgue 5, 387-428 (2022). MSC: 35Q55 35Q41 35R02 35A01 35A02 65M06 65N06 PDF BibTeX XML Cite \textit{C. Besse} et al., Ann. Henri Lebesgue 5, 387--428 (2022; Zbl 07524689) Full Text: DOI OpenURL
Dujardin, Guillaume; Lacroix-Violet, Ingrid High order linearly implicit methods for evolution equations. (English) Zbl 07523319 ESAIM, Math. Model. Numer. Anal. 56, No. 3, 743-766 (2022). MSC: 65M70 65N06 65L20 65L06 65M12 81Q05 35Q41 35Q55 35K05 PDF BibTeX XML Cite \textit{G. Dujardin} and \textit{I. Lacroix-Violet}, ESAIM, Math. Model. Numer. Anal. 56, No. 3, 743--766 (2022; Zbl 07523319) Full Text: DOI OpenURL
Poveda, Luis A.; Grave de Peralta, Luis; Pittman, Jacob; Poirier, Bill A non-relativistic approach to relativistic quantum mechanics: the case of the harmonic oscillator. (English) Zbl 07507684 Found. Phys. 52, No. 1, Paper No. 29, 20 p. (2022). MSC: 81Q05 81R20 81Q20 35P10 65N06 PDF BibTeX XML Cite \textit{L. A. Poveda} et al., Found. Phys. 52, No. 1, Paper No. 29, 20 p. (2022; Zbl 07507684) Full Text: DOI OpenURL
Jiang, Haiyan; Lu, Tiao; Zhang, Weitong A hybrid sinc-Galerkin/finite-difference method for the time-dependent Wigner equation. (English) Zbl 1487.81086 J. Comput. Appl. Math. 409, Article ID 114152, 12 p. (2022). MSC: 81Q05 65M70 81S30 45K05 82C70 81-10 PDF BibTeX XML Cite \textit{H. Jiang} et al., J. Comput. Appl. Math. 409, Article ID 114152, 12 p. (2022; Zbl 1487.81086) Full Text: DOI OpenURL
Arnold, Anton; Klein, Christian; Ujvari, Bernhard WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment. (English) Zbl 07489358 BIT 62, No. 1, 1-22 (2022). MSC: 65-XX 34L40 34E20 81Q20 PDF BibTeX XML Cite \textit{A. Arnold} et al., BIT 62, No. 1, 1--22 (2022; Zbl 07489358) Full Text: DOI arXiv OpenURL
Almushaira, Mustafa Fast high-accuracy compact conservative difference schemes for solving the nonlinear Schrödinger equation. (English) Zbl 1486.65092 J. Difference Equ. Appl. 28, No. 1, 10-38 (2022). MSC: 65M06 35J10 65T50 35Q55 35Q41 PDF BibTeX XML Cite \textit{M. Almushaira}, J. Difference Equ. Appl. 28, No. 1, 10--38 (2022; Zbl 1486.65092) Full Text: DOI OpenURL
Xu, Zhuangzhi; Cai, Wenjun; Hu, Dongdong; Wang, Yushun Exponential integrator preserving mass boundedness and energy conservation for nonlinear Schrödinger equation. (English) Zbl 1483.35228 Appl. Numer. Math. 173, 308-328 (2022). MSC: 35Q55 65M70 65M06 65N35 65M15 65M12 PDF BibTeX XML Cite \textit{Z. Xu} et al., Appl. Numer. Math. 173, 308--328 (2022; Zbl 1483.35228) Full Text: DOI OpenURL
Labidi, Samira; Omrani, Khaled A new conservative fourth-order accurate difference scheme for the nonlinear Schrödinger equation with wave operator. (English) Zbl 1486.65111 Appl. Numer. Math. 173, 1-12 (2022). MSC: 65M06 65N06 65M12 35Q55 35Q41 PDF BibTeX XML Cite \textit{S. Labidi} and \textit{K. Omrani}, Appl. Numer. Math. 173, 1--12 (2022; Zbl 1486.65111) Full Text: DOI OpenURL
Yi, Nianyu; Liu, Hailiang A mass- and energy-conserved DG method for the Schrödinger-Poisson equation. (English) Zbl 1483.35230 Numer. Algorithms 89, No. 2, 905-930 (2022). MSC: 35Q55 35Q60 65M60 65M06 65N30 65M15 65M12 PDF BibTeX XML Cite \textit{N. Yi} and \textit{H. Liu}, Numer. Algorithms 89, No. 2, 905--930 (2022; Zbl 1483.35230) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \textit{C. Jiang} et al., J. Sci. Comput. 90, No. 1, Paper No. 66, 27 p. (2022; Zbl 1481.65134) Full Text: DOI arXiv OpenURL
de la Hoz, Francisco; Kumar, Sandeep; Vega, Luis Vortex filament equation for a regular polygon in the hyperbolic plane. (English) Zbl 1483.35206 J. Nonlinear Sci. 32, No. 1, Paper No. 9, 34 p. (2022). MSC: 35Q55 28A80 65M06 65M20 65N06 65L06 PDF BibTeX XML Cite \textit{F. de la Hoz} et al., J. Nonlinear Sci. 32, No. 1, Paper No. 9, 34 p. (2022; Zbl 1483.35206) Full Text: DOI arXiv OpenURL
Ostermann, Alexander; Rousset, Frédéric; Schratz, Katharina Error estimates at low regularity of splitting schemes for NLS. (English) Zbl 1482.65197 Math. Comput. 91, No. 333, 169-182 (2022). Reviewer: Bülent Karasözen (Ankara) MSC: 65M70 65M06 65N35 65N30 65T50 65M12 65M15 35Q55 35Q41 PDF BibTeX XML Cite \textit{A. Ostermann} et al., Math. Comput. 91, No. 333, 169--182 (2022; Zbl 1482.65197) Full Text: DOI arXiv OpenURL
Kumar, Sandeep On the Schrödinger map for regular helical polygons in the hyperbolic space. (English) Zbl 07441038 Nonlinearity 35, No. 1, 84-109 (2022). MSC: 37D40 28A80 35Q55 65M06 65M20 53E30 PDF BibTeX XML Cite \textit{S. Kumar}, Nonlinearity 35, No. 1, 84--109 (2022; Zbl 07441038) Full Text: DOI arXiv OpenURL
Decleer, Pieter; Van Londersele, Arne; Rogier, Hendrik; Vande Ginste, Dries An alternating-direction hybrid implicit-explicit finite-difference time-domain method for the Schrödinger equation. (English) Zbl 1477.65132 J. Comput. Appl. Math. 403, Article ID 113881, 19 p. (2022). MSC: 65M06 35B35 35R20 35Q41 82D77 PDF BibTeX XML Cite \textit{P. Decleer} et al., J. Comput. Appl. Math. 403, Article ID 113881, 19 p. (2022; Zbl 1477.65132) Full Text: DOI OpenURL
Fan, Wenping; Jiang, Xiaoyun Error analysis of the unstructured mesh finite element method for the two-dimensional time-space fractional Schrödinger equation with a time-independent potential. (English) Zbl 07476638 Int. J. Comput. Math. 98, No. 8, 1663-1682 (2021). MSC: 65-XX 26A33 65M06 65M12 65M15 65M60 PDF BibTeX XML Cite \textit{W. Fan} and \textit{X. Jiang}, Int. J. Comput. Math. 98, No. 8, 1663--1682 (2021; Zbl 07476638) Full Text: DOI OpenURL
Hicdurmaz, Betul Finite difference schemes for time-fractional Schrödinger equations via fractional linear multistep method. (English) Zbl 1480.65209 Int. J. Comput. Math. 98, No. 8, 1561-1573 (2021). MSC: 65M06 35Q41 PDF BibTeX XML Cite \textit{B. Hicdurmaz}, Int. J. Comput. Math. 98, No. 8, 1561--1573 (2021; Zbl 1480.65209) Full Text: DOI OpenURL
Li, Shan; Wang, Tingchun; Wang, Jialing; Guo, Boling An efficient and accurate Fourier pseudo-spectral method for the nonlinear Schrödinger equation with wave operator. (English) Zbl 1480.65285 Int. J. Comput. Math. 98, No. 2, 340-356 (2021). MSC: 65M70 65M06 35Q55 65M12 65M15 PDF BibTeX XML Cite \textit{S. Li} et al., Int. J. Comput. Math. 98, No. 2, 340--356 (2021; Zbl 1480.65285) Full Text: DOI OpenURL
Destyl, Edès; Laminie, Jacques; Nuiro, Paul; Poullet, Pascal Numerical simulations of parity-time symmetric nonlinear Schrödinger equations in critical case. (English) Zbl 07451795 Discrete Contin. Dyn. Syst., Ser. S 14, No. 8, 2805-2821 (2021). MSC: 65-XX 35B40 35B44 35J10 35Q41 65M06 68N15 PDF BibTeX XML Cite \textit{E. Destyl} et al., Discrete Contin. Dyn. Syst., Ser. S 14, No. 8, 2805--2821 (2021; Zbl 07451795) Full Text: DOI OpenURL
Nagiyev, Sh. N.; Mir-Kasimov, R. M. Relativistic linear oscillator under the action of a constant external force. Wave functions and dynamical symmetry group. (English. Russian original) Zbl 1482.81012 Theor. Math. Phys. 208, No. 3, 1265-1276 (2021); translation from Teor. Mat. Fiz. 208, No. 3, 481-494 (2021). MSC: 81Q05 81R20 34C10 65L12 33C45 81S22 35P05 PDF BibTeX XML Cite \textit{Sh. N. Nagiyev} and \textit{R. M. Mir-Kasimov}, Theor. Math. Phys. 208, No. 3, 1265--1276 (2021; Zbl 1482.81012); translation from Teor. Mat. Fiz. 208, No. 3, 481--494 (2021) Full Text: DOI OpenURL
Ding, Zhiyan; Hajaiej, Hichem On a fractional Schrödinger equation in the presence of harmonic potential. (English) Zbl 1479.35772 Electron Res. Arch. 29, No. 5, 3449-3469 (2021). MSC: 35Q55 35Q41 35B35 35A01 35J60 47J30 65M70 65M06 26A33 35R11 PDF BibTeX XML Cite \textit{Z. Ding} and \textit{H. Hajaiej}, Electron Res. Arch. 29, No. 5, 3449--3469 (2021; Zbl 1479.35772) Full Text: DOI arXiv OpenURL
Yang, Yuna; Li, Hongwei; Guo, Xu A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator. (English) Zbl 07424130 Appl. Math. Comput. 404, Article ID 126234, 20 p. (2021). MSC: 65M06 65M12 65Z05 35Q55 PDF BibTeX XML Cite \textit{Y. Yang} et al., Appl. Math. Comput. 404, Article ID 126234, 20 p. (2021; Zbl 07424130) Full Text: DOI OpenURL
Frasca-Caccia, Gianluca; Hydon, Peter E. Numerical preservation of multiple local conservation laws. (English) Zbl 07423636 Appl. Math. Comput. 403, Article ID 126203, 23 p. (2021). MSC: 65M06 37K05 39A14 PDF BibTeX XML Cite \textit{G. Frasca-Caccia} and \textit{P. E. Hydon}, Appl. Math. Comput. 403, Article ID 126203, 23 p. (2021; Zbl 07423636) Full Text: DOI arXiv OpenURL
Caliari, Marco; Zuccher, Simone A fast time splitting finite difference approach to Gross-Pitaevskii equations. (English) Zbl 1473.65096 Commun. Comput. Phys. 29, No. 5, 1336-1364 (2021). MSC: 65M06 65M70 PDF BibTeX XML Cite \textit{M. Caliari} and \textit{S. Zuccher}, Commun. Comput. Phys. 29, No. 5, 1336--1364 (2021; Zbl 1473.65096) Full Text: DOI OpenURL
Zhao, Xiaofei Numerical integrators for continuous disordered nonlinear Schrödinger equation. (English) Zbl 1482.35222 J. Sci. Comput. 89, No. 2, Paper No. 40, 27 p. (2021). MSC: 35Q55 35Q41 35B65 65L20 65L70 65M06 65M12 65M15 65T50 65P10 60H40 82C44 35R60 PDF BibTeX XML Cite \textit{X. Zhao}, J. Sci. Comput. 89, No. 2, Paper No. 40, 27 p. (2021; Zbl 1482.35222) Full Text: DOI arXiv OpenURL
Kluczek, Mateusz; Andrade, David; Stiassnie, Michael On the Alber equation for shoaling water waves. (English) Zbl 1481.76100 J. Fluid Mech. 927, Paper No. R5, 11 p. (2021). MSC: 76E20 76B15 76M20 86A05 PDF BibTeX XML Cite \textit{M. Kluczek} et al., J. Fluid Mech. 927, Paper No. R5, 11 p. (2021; Zbl 1481.76100) Full Text: DOI OpenURL
Yang, Lei; Shen, Yedan; Hu, Zhicheng; Hu, Guanghui An implicit solver for the time-dependent Kohn-Sham equation. (English) Zbl 07404489 Numer. Math., Theory Methods Appl. 14, No. 1, 261-284 (2021). MSC: 65M55 65M50 65M60 65M06 65N30 35Q55 65Y05 PDF BibTeX XML Cite \textit{L. Yang} et al., Numer. Math., Theory Methods Appl. 14, No. 1, 261--284 (2021; Zbl 07404489) Full Text: DOI OpenURL
Deng, Beichuan; Shen, Jie; Zhuang, Qingqu Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis. (English) Zbl 07389366 J. Sci. Comput. 88, No. 3, Paper No. 69, 24 p. (2021). MSC: 65M70 65M06 65N35 65L06 65D30 65M12 65M15 35Q55 35Q41 PDF BibTeX XML Cite \textit{B. Deng} et al., J. Sci. Comput. 88, No. 3, Paper No. 69, 24 p. (2021; Zbl 07389366) Full Text: DOI OpenURL
Feng, Yue Improved error bounds of the Strang splitting method for the highly oscillatory fractional nonlinear Schrödinger equation. (English) Zbl 1479.35786 J. Sci. Comput. 88, No. 2, Paper No. 48, 24 p. (2021). MSC: 35Q55 35Q41 35B05 65M06 65N35 65M12 65M15 PDF BibTeX XML Cite \textit{Y. Feng}, J. Sci. Comput. 88, No. 2, Paper No. 48, 24 p. (2021; Zbl 1479.35786) Full Text: DOI OpenURL
Dodson, Benjamin; Soffer, Avraham; Spencer, Thomas Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in \(L^p\)-based Sobolev spaces. (English) Zbl 1476.35233 J. Math. Phys. 62, No. 7, 071507, 13 p. (2021). Reviewer: Johanna Michor (Wien) MSC: 35Q55 35Q41 35B65 35C08 35A01 35A02 37K40 65M06 65H10 82B20 82B26 PDF BibTeX XML Cite \textit{B. Dodson} et al., J. Math. Phys. 62, No. 7, 071507, 13 p. (2021; Zbl 1476.35233) Full Text: DOI arXiv OpenURL
Ashyralyev, Allaberen; Hicdurmaz, Betul Multidimensional problems for nonlinear fractional Schrödinger differential and difference equations. (English) Zbl 07376702 Math. Methods Appl. Sci. 44, No. 4, 2731-2751 (2021). MSC: 65M06 35R11 PDF BibTeX XML Cite \textit{A. Ashyralyev} and \textit{B. Hicdurmaz}, Math. Methods Appl. Sci. 44, No. 4, 2731--2751 (2021; Zbl 07376702) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \textit{G. Akrivis} and \textit{D. Li}, Calcolo 58, No. 2, Paper No. 17, 25 p. (2021; Zbl 1486.65158) Full Text: DOI OpenURL
Kang, Younghoon; Lee, Eunjung; Lee, Young-Ran Numerical solutions for one and two dimensional nonlinear problems related to dispersion managed solitons. (English) Zbl 1469.78052 J. Korean Math. Soc. 58, No. 4, 835-847 (2021). MSC: 78M20 65M06 65N25 35P20 35C08 78A60 35Q60 35Q55 35Q41 PDF BibTeX XML Cite \textit{Y. Kang} et al., J. Korean Math. Soc. 58, No. 4, 835--847 (2021; Zbl 1469.78052) Full Text: DOI OpenURL
Jiang, Haiyan; Lu, Tiao; Yin, Xu A hybrid explicit-implicit scheme for the time-dependent Wigner equation. (English) Zbl 1474.65277 J. Comput. Math. 39, No. 1, 22-42 (2021). MSC: 65M06 65M70 65M15 65M12 35Q40 81Q05 PDF BibTeX XML Cite \textit{H. Jiang} et al., J. Comput. Math. 39, No. 1, 22--42 (2021; Zbl 1474.65277) Full Text: DOI OpenURL
Hu, Hanzhang; Chen, Yanping Analysis of finite element two-grid algorithms for two-dimensional nonlinear Schrödinger equation with wave operator. (English) Zbl 1476.65241 J. Comput. Appl. Math. 397, Article ID 113647, 19 p. (2021). MSC: 65M60 65M06 65N30 65M12 65M15 65H10 65N50 35A01 35A02 35Q55 35Q41 PDF BibTeX XML Cite \textit{H. Hu} and \textit{Y. Chen}, J. Comput. Appl. Math. 397, Article ID 113647, 19 p. (2021; Zbl 1476.65241) Full Text: DOI OpenURL
Yokus, Asıf; Tuz, Münevver; Güngöz, Ufuk On the exact and numerical complex travelling wave solution to the nonlinear Schrödinger equation. (English) Zbl 07355103 J. Difference Equ. Appl. 27, No. 2, 195-206 (2021). MSC: 65L12 74S20 PDF BibTeX XML Cite \textit{A. Yokus} et al., J. Difference Equ. Appl. 27, No. 2, 195--206 (2021; Zbl 07355103) Full Text: DOI OpenURL
Muñoz-Pérez, Luis F.; Macías-Díaz, J. E. An implicit and convergent method for radially symmetric solutions of Higgs’ boson equation in the de Sitter space-time. (English) Zbl 1465.81040 Appl. Numer. Math. 165, 270-289 (2021). MSC: 81Q35 81V73 81V22 83C10 65M06 65Z05 35Q41 PDF BibTeX XML Cite \textit{L. F. Muñoz-Pérez} and \textit{J. E. Macías-Díaz}, Appl. Numer. Math. 165, 270--289 (2021; Zbl 1465.81040) Full Text: DOI OpenURL
Wang, Junjie High-order conservative schemes for the space fractional nonlinear Schrödinger equation. (English) Zbl 1475.65084 Appl. Numer. Math. 165, 248-269 (2021). MSC: 65M06 65N06 65B05 65M12 35Q55 35Q41 26A33 35R11 PDF BibTeX XML Cite \textit{J. Wang}, Appl. Numer. Math. 165, 248--269 (2021; Zbl 1475.65084) Full Text: DOI OpenURL
Fu, Yayun; Xu, Zhuangzhi; Cai, Wenjun; Wang, Yushun An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation. (English) Zbl 1475.65068 Appl. Numer. Math. 165, 232-247 (2021). MSC: 65M06 65N35 35Q55 35Q41 26A33 35R11 PDF BibTeX XML Cite \textit{Y. Fu} et al., Appl. Numer. Math. 165, 232--247 (2021; Zbl 1475.65068) Full Text: DOI OpenURL
Yang, Yin; Li, Xueyang; Xiao, Aiguo Fourier pseudospectral method for fractional stationary Schrödinger equation. (English) Zbl 1468.35189 Appl. Numer. Math. 165, 137-151 (2021). MSC: 35Q55 35Q40 65M06 65T50 35R11 PDF BibTeX XML Cite \textit{Y. Yang} et al., Appl. Numer. Math. 165, 137--151 (2021; Zbl 1468.35189) Full Text: DOI OpenURL
Lin, Chia-Liang; Simos, T. E. A new finite difference method with optimal phase and stability properties for problems in chemistry. (English) Zbl 1467.65074 J. Math. Chem. 59, No. 4, 951-984 (2021). MSC: 65L12 65L05 65L10 35Q55 PDF BibTeX XML Cite \textit{C.-L. Lin} and \textit{T. E. Simos}, J. Math. Chem. 59, No. 4, 951--984 (2021; Zbl 1467.65074) Full Text: DOI OpenURL
Yan, Jingye; Zhang, Hong; Qian, Xu; Song, Songhe Regularised finite difference methods for the logarithmic Klein-Gordon equation. (English) Zbl 1464.35275 East Asian J. Appl. Math. 11, No. 1, 119-142 (2021). MSC: 35Q40 65M06 65N06 65M15 65M12 81Q05 PDF BibTeX XML Cite \textit{J. Yan} et al., East Asian J. Appl. Math. 11, No. 1, 119--142 (2021; Zbl 1464.35275) Full Text: DOI arXiv OpenURL
Hong, Younghun; Kwak, Chulkwang; Nakamura, Shohei; Yang, Changhun Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations. (English) Zbl 1464.35324 J. Evol. Equ. 21, No. 1, 391-418 (2021). MSC: 35Q55 81T27 65M06 34L40 PDF BibTeX XML Cite \textit{Y. Hong} et al., J. Evol. Equ. 21, No. 1, 391--418 (2021; Zbl 1464.35324) Full Text: DOI arXiv OpenURL
Besse, Christophe; Descombes, Stéphane; Dujardin, Guillaume; Lacroix-Violet, Ingrid Energy-preserving methods for nonlinear Schrödinger equations. (English) Zbl 1460.65099 IMA J. Numer. Anal. 41, No. 1, 618-653 (2021). MSC: 65M06 65M12 35Q55 35Q41 65F10 PDF BibTeX XML Cite \textit{C. Besse} et al., IMA J. Numer. Anal. 41, No. 1, 618--653 (2021; Zbl 1460.65099) Full Text: DOI arXiv OpenURL
Li, Jiyong; Wang, Tingchun Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation. (English) Zbl 1457.81035 Appl. Numer. Math. 162, 150-170 (2021). MSC: 81Q05 81R20 35Q55 65L12 35R20 81R05 35G30 81-10 PDF BibTeX XML Cite \textit{J. Li} and \textit{T. Wang}, Appl. Numer. Math. 162, 150--170 (2021; Zbl 1457.81035) Full Text: DOI OpenURL
Krämer, Patrick; Schratz, Katharina; Zhao, Xiaofei Splitting methods for nonlinear Dirac equations with Thirring type interaction in the nonrelativistic limit regime. (English) Zbl 1457.78006 J. Comput. Appl. Math. 387, Article ID 112494, 16 p. (2021). MSC: 78A35 78M20 78M22 65M06 65N35 65M12 65M15 81Q05 35Q41 PDF BibTeX XML Cite \textit{P. Krämer} et al., J. Comput. Appl. Math. 387, Article ID 112494, 16 p. (2021; Zbl 1457.78006) Full Text: DOI Link OpenURL
Lorin, Emmanuel Numerical analysis of the exact factorization of molecular time-dependent Schrödinger wavefunctions. (English) Zbl 1459.65152 Commun. Nonlinear Sci. Numer. Simul. 95, Article ID 105627, 22 p. (2021). MSC: 65M06 65M12 35Q55 PDF BibTeX XML Cite \textit{E. Lorin}, Commun. Nonlinear Sci. Numer. Simul. 95, Article ID 105627, 22 p. (2021; Zbl 1459.65152) Full Text: DOI OpenURL
Cui, Jin; Xu, Zhuangzhi; Wang, Yushun; Jiang, Chaolong Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation. (English) Zbl 1454.65058 Appl. Math. Lett. 112, Article ID 106770, 8 p. (2021). Reviewer: Bülent Karasözen (Ankara) MSC: 65M06 65L06 65P10 35A22 35Q55 PDF BibTeX XML Cite \textit{J. Cui} et al., Appl. Math. Lett. 112, Article ID 106770, 8 p. (2021; Zbl 1454.65058) Full Text: DOI arXiv OpenURL
Schratz, Katharina; Wang, Yan; Zhao, Xiaofei Low-regularity integrators for nonlinear Dirac equations. (English) Zbl 1450.35231 Math. Comput. 90, No. 327, 189-214 (2021). MSC: 35Q41 65M70 65N35 65M12 65M15 65M06 35B65 35S30 PDF BibTeX XML Cite \textit{K. Schratz} et al., Math. Comput. 90, No. 327, 189--214 (2021; Zbl 1450.35231) Full Text: DOI arXiv OpenURL
Xing, F. New optimized Schwarz algorithms for one dimensional Schrödinger equation with general potential. (English) Zbl 1456.65177 J. Comput. Appl. Math. 383, Article ID 113018, 12 p. (2021). MSC: 65N55 65M55 65M06 65F05 65F08 65F10 65Y05 35Q55 PDF BibTeX XML Cite \textit{F. Xing}, J. Comput. Appl. Math. 383, Article ID 113018, 12 p. (2021; Zbl 1456.65177) Full Text: DOI arXiv OpenURL
Decleer, Pieter; Van Londersele, Arne; Rogier, Hendrik; Vande Ginste, Dries Nonuniform and higher-order FDTD methods for the Schrödinger equation. (English) Zbl 1465.65069 J. Comput. Appl. Math. 381, Article ID 113023, 18 p. (2021). MSC: 65M06 65N06 65M12 65M15 78A25 78M20 35Q41 PDF BibTeX XML Cite \textit{P. Decleer} et al., J. Comput. Appl. Math. 381, Article ID 113023, 18 p. (2021; Zbl 1465.65069) Full Text: DOI OpenURL
Fei, Mingfa; Zhang, Guoyu; Wang, Nan; Huang, Chengming A linearized conservative Galerkin-Legendre spectral method for the strongly coupled nonlinear fractional Schrödinger equations. (English) Zbl 1487.65164 Adv. Difference Equ. 2020, Paper No. 661, 23 p. (2020). MSC: 65M70 65M06 65M12 35R11 35Q55 PDF BibTeX XML Cite \textit{M. Fei} et al., Adv. Difference Equ. 2020, Paper No. 661, 23 p. (2020; Zbl 1487.65164) Full Text: DOI OpenURL
Chang, Yan; Chen, Huanzhen Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations. (English) Zbl 1487.65113 Adv. Difference Equ. 2020, Paper No. 4, 18 p. (2020). MSC: 65M06 35R11 65M12 PDF BibTeX XML Cite \textit{Y. Chang} and \textit{H. Chen}, Adv. Difference Equ. 2020, Paper No. 4, 18 p. (2020; Zbl 1487.65113) Full Text: DOI OpenURL
Ding, Qinxu; Wong, Patricia J. Y. Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation. (English) Zbl 1486.65018 Adv. Difference Equ. 2020, Paper No. 577, 26 p. (2020). MSC: 65D07 35R11 65M06 65M12 35Q55 26A33 PDF BibTeX XML Cite \textit{Q. Ding} and \textit{P. J. Y. Wong}, Adv. Difference Equ. 2020, Paper No. 577, 26 p. (2020; Zbl 1486.65018) Full Text: DOI OpenURL
Eskar, Rena; Feng, Xinlong; Kasim, Ehmet On high-order compact schemes for the multidimensional time-fractional Schrödinger equation. (English) Zbl 1486.65101 Adv. Difference Equ. 2020, Paper No. 492, 17 p. (2020). MSC: 65M06 65M12 26A33 65M70 35R11 PDF BibTeX XML Cite \textit{R. Eskar} et al., Adv. Difference Equ. 2020, Paper No. 492, 17 p. (2020; Zbl 1486.65101) Full Text: DOI OpenURL
Kriauzienė, Rima; Bugajev, Andrej; Čiegis, Raimondas A three-level parallelisation scheme and application to the Nelder-Mead algorithm. (English) Zbl 1476.65175 Math. Model. Anal. 25, No. 4, 584-607 (2020). MSC: 65M06 65Y05 35Q56 65M12 PDF BibTeX XML Cite \textit{R. Kriauzienė} et al., Math. Model. Anal. 25, No. 4, 584--607 (2020; Zbl 1476.65175) Full Text: DOI arXiv OpenURL
Antoine, Xavier; Lorin, Emmanuel Explicit computation of Robin parameters in optimized Schwarz waveform relaxation methods for Schrödinger equations based on pseudodifferential operators. (English) Zbl 1473.65180 Commun. Comput. Phys. 27, No. 4, 1032-1052 (2020). MSC: 65M55 65M60 65M06 35S10 PDF BibTeX XML Cite \textit{X. Antoine} and \textit{E. Lorin}, Commun. Comput. Phys. 27, No. 4, 1032--1052 (2020; Zbl 1473.65180) Full Text: DOI OpenURL
He, Zengjia; Kong, Linghua; Fu, Fangfang The splitting high-order compact difference scheme for two-dimensional Gross-Pitaevskii equation. (Chinese. English summary) Zbl 1474.65276 J. Jiangxi Norm. Univ., Nat. Sci. Ed. 44, No. 6, 599-603 (2020). MSC: 65M06 65N06 65M12 65N12 35Q55 PDF BibTeX XML Cite \textit{Z. He} et al., J. Jiangxi Norm. Univ., Nat. Sci. Ed. 44, No. 6, 599--603 (2020; Zbl 1474.65276) Full Text: DOI OpenURL
Ma, Ying; Chen, Lizhen A Jacobi-Galerkin spectral method for computing the ground and first excited states of nonlinear fractional Schrödinger equation. (English) Zbl 1468.65166 East Asian J. Appl. Math. 10, No. 2, 274-294 (2020). MSC: 65M70 65M06 65N35 65N30 65N25 35Q41 35Q55 35R11 PDF BibTeX XML Cite \textit{Y. Ma} and \textit{L. Chen}, East Asian J. Appl. Math. 10, No. 2, 274--294 (2020; Zbl 1468.65166) Full Text: DOI OpenURL
Izadi, Fanoosh; Saberinajafi, Hashem; Refahi Sheikhani, A. H. The numerical solution of Fisher equation: a nonstandard finite difference in conjunction with Richtmyer formula. (English) Zbl 1474.35234 Comput. Methods Differ. Equ. 8, No. 2, 330-346 (2020). MSC: 35J05 35J10 35K05 35L05 PDF BibTeX XML Cite \textit{F. Izadi} et al., Comput. Methods Differ. Equ. 8, No. 2, 330--346 (2020; Zbl 1474.35234) Full Text: DOI OpenURL
Ashyralyev, Allaberen; Hicdurmaz, Betul Bounded solutions of second order of accuracy difference schemes for semilinear fractional Schrödinger equations. (English) Zbl 1474.35634 Fract. Calc. Appl. Anal. 23, No. 6, 1723-1761 (2020). MSC: 35R11 65M06 26A33 PDF BibTeX XML Cite \textit{A. Ashyralyev} and \textit{B. Hicdurmaz}, Fract. Calc. Appl. Anal. 23, No. 6, 1723--1761 (2020; Zbl 1474.35634) Full Text: DOI OpenURL
Wang, Pengde; Xu, Zhiguo; Yin, Jia Simple high-order boundary conditions for computing rogue waves in the nonlinear Schrödinger equation. (English) Zbl 1456.35188 Comput. Phys. Commun. 251, Article ID 107109, 13 p. (2020). MSC: 35Q55 35C08 PDF BibTeX XML Cite \textit{P. Wang} et al., Comput. Phys. Commun. 251, Article ID 107109, 13 p. (2020; Zbl 1456.35188) Full Text: DOI OpenURL
Dohnal, Tomáš; Rudolf, Daniel NLS approximation for wavepackets in periodic cubically nonlinear wave problems in \(\mathbb{R}^d\). (English) Zbl 1459.35342 Appl. Anal. 99, No. 10, 1685-1723 (2020). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35Q60 35L71 41A60 35C08 65N25 65N06 65L06 65T50 PDF BibTeX XML Cite \textit{T. Dohnal} and \textit{D. Rudolf}, Appl. Anal. 99, No. 10, 1685--1723 (2020; Zbl 1459.35342) Full Text: DOI arXiv OpenURL
Wang, Jianyun; Jin, Jicheng; Tian, Zhikun Two-grid finite element method with Crank-Nicolson fully discrete scheme for the time-dependent Schrödinger equation. (English) Zbl 1463.65281 Numer. Math., Theory Methods Appl. 13, No. 2, 334-352 (2020). MSC: 65M55 65M60 65M15 65M12 65M06 65N30 35J05 PDF BibTeX XML Cite \textit{J. Wang} et al., Numer. Math., Theory Methods Appl. 13, No. 2, 334--352 (2020; Zbl 1463.65281) Full Text: DOI OpenURL
Li, Desheng; Li, Hua A conservative difference scheme for nonlinear fourth-order Schrödinger equation. (Chinese. English summary) Zbl 1463.65230 J. Shenyang Norm. Univ., Nat. Sci. 38, No. 3, 256-260 (2020). MSC: 65M06 65M12 35Q55 PDF BibTeX XML Cite \textit{D. Li} and \textit{H. Li}, J. Shenyang Norm. Univ., Nat. Sci. 38, No. 3, 256--260 (2020; Zbl 1463.65230) Full Text: DOI OpenURL
Li, Yongsheng; Xiang, Shaoting; Fu, Yiping Numerical solution to a kind of the nonlinear Schrödinger equation. (Chinese. English summary) Zbl 1463.65236 J. Henan Norm. Univ., Nat. Sci. 48, No. 5, 22-30 (2020). MSC: 65M06 65M12 35Q55 PDF BibTeX XML Cite \textit{Y. Li} et al., J. Henan Norm. Univ., Nat. Sci. 48, No. 5, 22--30 (2020; Zbl 1463.65236) Full Text: DOI OpenURL
Cheng, Bin; Chen, Ya-Ming; Xu, Chuan-Fu; Li, Da-Li; Deng, Xiao-Gang Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method. (English) Zbl 1451.35181 Commun. Theor. Phys. 72, No. 2, Article ID 025001, 6 p. (2020). MSC: 35Q55 81Q05 PDF BibTeX XML Cite \textit{B. Cheng} et al., Commun. Theor. Phys. 72, No. 2, Article ID 025001, 6 p. (2020; Zbl 1451.35181) Full Text: DOI OpenURL
Gladkikh, A. A.; Malinetskiĭ, G. G. Nonlinear Dirac equation for graphene. (Russian. English summary) Zbl 1454.35312 Mat. Model. 32, No. 8, 43-56 (2020). MSC: 35Q41 82D80 82D40 65M06 PDF BibTeX XML Cite \textit{A. A. Gladkikh} and \textit{G. G. Malinetskiĭ}, Mat. Model. 32, No. 8, 43--56 (2020; Zbl 1454.35312) Full Text: DOI MNR OpenURL
Ji, Bingquan; Zhang, Luming Error estimates of a conservative finite difference Fourier pseudospectral method for the Klein-Gordon-Schrödinger equation. (English) Zbl 1453.65222 Comput. Math. Appl. 79, No. 7, 1956-1971 (2020). MSC: 65M06 65M70 65M15 35Q55 65T50 PDF BibTeX XML Cite \textit{B. Ji} and \textit{L. Zhang}, Comput. Math. Appl. 79, No. 7, 1956--1971 (2020; Zbl 1453.65222) Full Text: DOI OpenURL
Rena, Eskar; Huang, Pengzhan; Feng, Xinlong Sixth-order compact ADI splitting method for the nonlinear Schrödinger equation in three-dimensions. (Chinese. English summary) Zbl 1463.65242 Math. Pract. Theory 50, No. 1, 229-237 (2020). MSC: 65M06 65M12 35Q55 PDF BibTeX XML Cite \textit{E. Rena} et al., Math. Pract. Theory 50, No. 1, 229--237 (2020; Zbl 1463.65242) OpenURL
Ashi, Hala A.; Aljahdaly, Noufe H. Breather and solitons waves in optical fibers via exponential time differencing method. (English) Zbl 1452.65146 Commun. Nonlinear Sci. Numer. Simul. 85, Article ID 105237, 7 p. (2020). MSC: 65M06 65M99 78A60 78M20 35C08 35Q55 35Q41 PDF BibTeX XML Cite \textit{H. A. Ashi} and \textit{N. H. Aljahdaly}, Commun. Nonlinear Sci. Numer. Simul. 85, Article ID 105237, 7 p. (2020; Zbl 1452.65146) Full Text: DOI OpenURL
Wang, Zenggui; Simos, T. E. A finite difference method with zero phase-lag and its derivatives for quantum chemistry problems. (English) Zbl 1448.81315 J. Math. Chem. 58, No. 8, 1680-1710 (2020). MSC: 81Q05 81V55 35G10 65M06 81-08 PDF BibTeX XML Cite \textit{Z. Wang} and \textit{T. E. Simos}, J. Math. Chem. 58, No. 8, 1680--1710 (2020; Zbl 1448.81315) Full Text: DOI OpenURL
Mauser, Norbert J.; Zhang, Yong; Zhao, Xiaofei On the rotating nonlinear Klein-Gordon equation: nonrelativistic limit and numerical methods. (English) Zbl 1446.65074 Multiscale Model. Simul. 18, No. 2, 999-1024 (2020). MSC: 65M06 65M70 65Z99 81Q05 85A40 35Q55 35Q40 82D50 PDF BibTeX XML Cite \textit{N. J. Mauser} et al., Multiscale Model. Simul. 18, No. 2, 999--1024 (2020; Zbl 1446.65074) Full Text: DOI OpenURL
Deuflhard, Peter; Weiser, Martin Numerical mathematics 3: Adaptive numerical solution of partial differential equations. 2nd expanded edition. (Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen.) (German) Zbl 1451.65002 De Gruyter Studium. Berlin: De Gruyter (ISBN 978-3-11-069168-9/pbk; 978-3-11-068965-5/ebook). xvi, 456 p. (2020). MSC: 65-01 65N22 65M22 65M15 65M60 65N15 65N30 65N12 65F05 65F08 65N55 65N50 65N06 65N35 65Y15 35J05 35J60 35L05 35Q41 35Q30 35Q61 PDF BibTeX XML Cite \textit{P. Deuflhard} and \textit{M. Weiser}, Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen. 2nd expanded edition. Berlin: De Gruyter (2020; Zbl 1451.65002) Full Text: DOI OpenURL
Pan, Kejia; Xia, Junyi; He, Dongdong; Zhang, Qifeng A three-level linearized difference scheme for nonlinear Schrödinger equation with absorbing boundary conditions. (English) Zbl 1442.65172 Appl. Numer. Math. 156, 32-49 (2020). MSC: 65M06 65M12 35Q55 PDF BibTeX XML Cite \textit{K. Pan} et al., Appl. Numer. Math. 156, 32--49 (2020; Zbl 1442.65172) Full Text: DOI OpenURL
Li, Meng; Huang, Chengming; Zhao, Yongliang Fast conservative numerical algorithm for the coupled fractional Klein-Gordon-Schrödinger equation. (English) Zbl 1442.65168 Numer. Algorithms 84, No. 3, 1081-1119 (2020). MSC: 65M06 65N30 65M12 65F10 65F08 65T50 15B05 26A33 35R11 35Q55 PDF BibTeX XML Cite \textit{M. Li} et al., Numer. Algorithms 84, No. 3, 1081--1119 (2020; Zbl 1442.65168) Full Text: DOI OpenURL
Cai, Jiaxiang; Zhang, Haihui Efficient schemes for the damped nonlinear Schrödinger equation in high dimensions. (English) Zbl 1465.65067 Appl. Math. Lett. 102, Article ID 106158, 7 p. (2020). MSC: 65M06 65M20 65T50 65H10 65P10 35Q55 PDF BibTeX XML Cite \textit{J. Cai} and \textit{H. Zhang}, Appl. Math. Lett. 102, Article ID 106158, 7 p. (2020; Zbl 1465.65067) Full Text: DOI OpenURL
Li, Xin; Zhang, Luming An efficient spectral-collocation difference method for two-dimensional Schrödinger equation with Neumann boundary conditions. (English) Zbl 1437.65214 Comput. Math. Appl. 79, No. 8, 2322-2335 (2020). MSC: 65N35 65M06 65T50 35Q55 35Q41 PDF BibTeX XML Cite \textit{X. Li} and \textit{L. Zhang}, Comput. Math. Appl. 79, No. 8, 2322--2335 (2020; Zbl 1437.65214) Full Text: DOI OpenURL
Zhang, Houchao; Shi, Dongyang; Li, Qingfu Nonconforming finite element method for a generalized nonlinear Schrödinger equation. (English) Zbl 1474.65375 Appl. Math. Comput. 377, Article ID 125141, 20 p. (2020). MSC: 65M60 65M06 65N30 65M15 65M12 35Q55 PDF BibTeX XML Cite \textit{H. Zhang} et al., Appl. Math. Comput. 377, Article ID 125141, 20 p. (2020; Zbl 1474.65375) Full Text: DOI OpenURL
Abbaszadeh, Mostafa; Dehghan, Mehdi Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation. (English) Zbl 1437.65174 Appl. Numer. Math. 154, 172-186 (2020). MSC: 65N30 65N15 65M06 65M12 35Q55 PDF BibTeX XML Cite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Numer. Math. 154, 172--186 (2020; Zbl 1437.65174) Full Text: DOI OpenURL
Jiang, Chaolong; Song, Yongzhong; Wang, Yushun A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions. (English) Zbl 1436.65148 Adv. Comput. Math. 46, No. 2, Paper No. 23, 31 p. (2020). MSC: 65M70 65M06 65M12 65M15 35Q55 PDF BibTeX XML Cite \textit{C. Jiang} et al., Adv. Comput. Math. 46, No. 2, Paper No. 23, 31 p. (2020; Zbl 1436.65148) Full Text: DOI arXiv OpenURL
Li, Hao-chen; Sun, Jian-qiang; Ye, Hang; He, Xue-jun Dispersion analysis of multi-symplectic scheme for the nonlinear Schrödinger equations. (English) Zbl 1483.65139 Acta Math. Appl. Sin., Engl. Ser. 36, No. 2, 503-515 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 65M06 35Q55 65P10 PDF BibTeX XML Cite \textit{H.-c. Li} et al., Acta Math. Appl. Sin., Engl. Ser. 36, No. 2, 503--515 (2020; Zbl 1483.65139) Full Text: DOI OpenURL
Fei, Mingfa; Wang, Nan; Huang, Chengming; Ma, Xiaohua A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation. (English) Zbl 1436.65099 Appl. Numer. Math. 153, 399-411 (2020). MSC: 65M06 65M12 35Q41 35R11 26A33 PDF BibTeX XML Cite \textit{M. Fei} et al., Appl. Numer. Math. 153, 399--411 (2020; Zbl 1436.65099) Full Text: DOI OpenURL
Hu, Yunxia; Li, Hongwei; Jiang, Ziwen Efficient semi-implicit compact finite difference scheme for nonlinear Schrödinger equations on unbounded domain. (English) Zbl 1436.65103 Appl. Numer. Math. 153, 319-343 (2020). MSC: 65M06 35Q41 35Q55 PDF BibTeX XML Cite \textit{Y. Hu} et al., Appl. Numer. Math. 153, 319--343 (2020; Zbl 1436.65103) Full Text: DOI OpenURL
Wang, Wansheng; Tang, Jiao Efficient exponential splitting spectral methods for linear Schrödinger equation in the semiclassical regime. (English) Zbl 1437.65153 Appl. Numer. Math. 153, 132-146 (2020). MSC: 65M70 65M06 65N35 65M15 35Q41 PDF BibTeX XML Cite \textit{W. Wang} and \textit{J. Tang}, Appl. Numer. Math. 153, 132--146 (2020; Zbl 1437.65153) Full Text: DOI OpenURL
Cheng, Bianru; Wang, Dongling; Yang, Wei Energy preserving relaxation method for space-fractional nonlinear Schrödinger equation. (English) Zbl 1440.65084 Appl. Numer. Math. 152, 480-498 (2020). MSC: 65M06 65N35 65M12 65M15 35Q55 26A33 35R11 PDF BibTeX XML Cite \textit{B. Cheng} et al., Appl. Numer. Math. 152, 480--498 (2020; Zbl 1440.65084) Full Text: DOI HAL OpenURL
Li, Xiang-Gui; Cai, Yongyong; Wang, Pengde Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation. (English) Zbl 1440.65090 Appl. Numer. Math. 151, 337-353 (2020). MSC: 65M06 65N06 65M12 65M15 35Q55 82B10 PDF BibTeX XML Cite \textit{X.-G. Li} et al., Appl. Numer. Math. 151, 337--353 (2020; Zbl 1440.65090) Full Text: DOI OpenURL
Hao, Sheng; Simos, T. E. A phase fitted FinDiff process for DifEquns in quantum chemistry. (English) Zbl 1433.81079 J. Math. Chem. 58, No. 2, 353-381 (2020). MSC: 81Q05 65L05 81V55 65M06 PDF BibTeX XML Cite \textit{S. Hao} and \textit{T. E. Simos}, J. Math. Chem. 58, No. 2, 353--381 (2020; Zbl 1433.81079) Full Text: DOI OpenURL
Chen, Anqi; Cheng, Yingda; Liu, Yong; Zhang, Mengping Superconvergence of ultra-weak discontinuous Galerkin methods for the linear Schrödinger equation in one dimension. (English) Zbl 1440.65131 J. Sci. Comput. 82, No. 1, Paper No. 22, 44 p. (2020). MSC: 65M60 65M06 65M12 65M15 35Q41 PDF BibTeX XML Cite \textit{A. Chen} et al., J. Sci. Comput. 82, No. 1, Paper No. 22, 44 p. (2020; Zbl 1440.65131) Full Text: DOI arXiv OpenURL
Li, Meng; Huang, Chengming; Ming, Wanyuan A relaxation-type Galerkin FEM for nonlinear fractional Schrödinger equations. (English) Zbl 1434.65186 Numer. Algorithms 83, No. 1, 99-124 (2020). MSC: 65M60 65M06 35R11 65M12 47H40 35Q41 PDF BibTeX XML Cite \textit{M. Li} et al., Numer. Algorithms 83, No. 1, 99--124 (2020; Zbl 1434.65186) Full Text: DOI OpenURL
Mackenzie, J. A.; Mekwi, W. R. An \(hr\)-adaptive method for the cubic nonlinear Schrödinger equation. (English) Zbl 1431.65163 J. Comput. Appl. Math. 364, Article ID 112320, 20 p. (2020). MSC: 65M50 65M06 65M25 65M12 35Q55 35Q41 PDF BibTeX XML Cite \textit{J. A. Mackenzie} and \textit{W. R. Mekwi}, J. Comput. Appl. Math. 364, Article ID 112320, 20 p. (2020; Zbl 1431.65163) Full Text: DOI arXiv OpenURL
Jha, Navnit; Singh, Bhagat Exponential basis and exponential expanding grids third (fourth)-order compact schemes for nonlinear three-dimensional convection-diffusion-reaction equation. (English) Zbl 1485.65114 Adv. Difference Equ. 2019, Paper No. 339, 27 p. (2019). MSC: 65N06 65N12 65F10 35J25 35J65 PDF BibTeX XML Cite \textit{N. Jha} and \textit{B. Singh}, Adv. Difference Equ. 2019, Paper No. 339, 27 p. (2019; Zbl 1485.65114) Full Text: DOI OpenURL
Zhang, Hui; Jiang, Xiaoyun; Wang, Chu; Chen, Shanzhen Crank-Nicolson Fourier spectral methods for the space fractional nonlinear Schrödinger equation and its parameter estimation. (English) Zbl 07474802 Int. J. Comput. Math. 96, No. 2, 238-263 (2019). MSC: 26A33 65M06 65M12 65M15 65M70 PDF BibTeX XML Cite \textit{H. Zhang} et al., Int. J. Comput. Math. 96, No. 2, 238--263 (2019; Zbl 07474802) Full Text: DOI OpenURL
Ahsan, Muhammad; Ahmad, Imtiaz; Ahmad, Masood; Hussian, Iltaf A numerical Haar wavelet-finite difference hybrid method for linear and non-linear Schrödinger equation. (English) Zbl 07316734 Math. Comput. Simul. 165, 13-25 (2019). MSC: 65Txx 45Gxx 65Rxx PDF BibTeX XML Cite \textit{M. Ahsan} et al., Math. Comput. Simul. 165, 13--25 (2019; Zbl 07316734) Full Text: DOI OpenURL
Trofimov, Vyacheslav A.; Trykin, Evgeny M. Enhancement of ABCs efficiency at computer simulation of optical pulse interaction with inhomogeneous nonlinear medium. (English) Zbl 1453.65235 J. Comput. Phys. 399, Article ID 108947, 19 p. (2019). MSC: 65M06 65Z05 35Q60 35Q55 78A60 PDF BibTeX XML Cite \textit{V. A. Trofimov} and \textit{E. M. Trykin}, J. Comput. Phys. 399, Article ID 108947, 19 p. (2019; Zbl 1453.65235) Full Text: DOI OpenURL
Bao, Weizhu; Zhao, Xiaofei Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime. (English) Zbl 1453.65278 J. Comput. Phys. 398, Article ID 108886, 30 p. (2019). MSC: 65M15 65M06 35Q40 81Q05 65Z05 PDF BibTeX XML Cite \textit{W. Bao} and \textit{X. Zhao}, J. Comput. Phys. 398, Article ID 108886, 30 p. (2019; Zbl 1453.65278) Full Text: DOI arXiv OpenURL
Nekrasov, S. A.; Chernoivan, D. N. Quantum modeling of the electrical double layer. (Russian. English summary) Zbl 1439.82049 Mat. Model. 31, No. 1, 27-43 (2019). MSC: 82D10 82M20 35Q55 81V10 82-10 PDF BibTeX XML Cite \textit{S. A. Nekrasov} and \textit{D. N. Chernoivan}, Mat. Model. 31, No. 1, 27--43 (2019; Zbl 1439.82049) Full Text: DOI MNR OpenURL
Negulescu, Claudia Analytical and numerical aspects of the linear and nonlinear Schrödinger equation. (English) Zbl 1441.35207 Riv. Mat. Univ. Parma (N.S.) 10, No. 2, 351-446 (2019). MSC: 35Q41 35Q55 42B20 65L20 65M06 81S22 35B25 35B40 PDF BibTeX XML Cite \textit{C. Negulescu}, Riv. Mat. Univ. Parma (N.S.) 10, No. 2, 351--446 (2019; Zbl 1441.35207) OpenURL
Miyatake, Yuto; Nakagawa, Tai; Sogabe, Tomohiro; Zhang, Shao-Liang A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation. (English) Zbl 1434.65207 J. Comput. Dyn. 6, No. 2, 361-383 (2019). MSC: 65M70 65F08 65N22 65M06 65F10 35R11 35Q91 81S40 PDF BibTeX XML Cite \textit{Y. Miyatake} et al., J. Comput. Dyn. 6, No. 2, 361--383 (2019; Zbl 1434.65207) Full Text: DOI arXiv OpenURL