Liu, Sheng-en; Ge, Yongbin; Wang, Shuaikang Conservative higher-order finite difference scheme for the coupled nonlinear Schrödinger equations. (English) Zbl 07810006 Commun. Nonlinear Sci. Numer. Simul. 131, Article ID 107797, 20 p. (2024). MSC: 65M06 65N06 65M12 65M15 65B05 78A60 35Q55 35Q41 35Q60 PDFBibTeX XMLCite \textit{S.-e. Liu} et al., Commun. Nonlinear Sci. Numer. Simul. 131, Article ID 107797, 20 p. (2024; Zbl 07810006) Full Text: DOI
Li, Meng; Zhao, Jikun; Chen, Shaochun Unconditional error analysis of VEMs for a generalized nonlinear Schrödinger equation. (English) Zbl 07806682 J. Comput. Math. 42, No. 2, 500-543 (2024). MSC: 65N35 65N12 76D07 65N15 PDFBibTeX XMLCite \textit{M. Li} et al., J. Comput. Math. 42, No. 2, 500--543 (2024; Zbl 07806682) Full Text: DOI
Li, Dongfang; Li, Xiaoxi; Sun, Hai-wei Optimal error estimates of SAV Crank-Nicolson finite element method for the coupled nonlinear Schrödinger equation. (English) Zbl 07766141 J. Sci. Comput. 97, No. 3, Paper No. 71, 26 p. (2023). MSC: 65F35 15A12 15A18 PDFBibTeX XMLCite \textit{D. Li} et al., J. Sci. Comput. 97, No. 3, Paper No. 71, 26 p. (2023; Zbl 07766141) Full Text: DOI
Bian, Shasha; Pei, Yitong; Guo, Boling Numerical simulation of a generalized nonlinear derivative Schrödinger equation. (English) Zbl 1512.78027 Electron. Res. Arch. 30, No. 8, 3130-3152 (2022). MSC: 78A60 35Q55 35Q41 35C08 78M20 65M06 65M12 41A25 PDFBibTeX XMLCite \textit{S. Bian} et al., Electron. Res. Arch. 30, No. 8, 3130--3152 (2022; Zbl 1512.78027) Full Text: DOI
Dangskul, Supreedee; Suebcharoen, Teeranush Evaluation of shallow water waves modelled by the Rosenau-Kawahara equation using pseudo-compact finite difference approach. (English) Zbl 1513.65436 Int. J. Comput. Math. 99, No. 8, 1617-1637 (2022). MSC: 65N06 65M12 65M06 35C08 35B05 35Q35 PDFBibTeX XMLCite \textit{S. Dangskul} and \textit{T. Suebcharoen}, Int. J. Comput. Math. 99, No. 8, 1617--1637 (2022; Zbl 1513.65436) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi A class of moving kriging interpolation-based DQ methods to simulate multi-dimensional space Galilei invariant fractional advection-diffusion equation. (English) Zbl 07512665 Numer. Algorithms 90, No. 1, 271-299 (2022). MSC: 65M99 35R11 65M06 65M70 65M12 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Numer. Algorithms 90, No. 1, 271--299 (2022; Zbl 07512665) Full Text: DOI
Zhai, Liangliang; Wang, Junjie High-order conservative scheme for the coupled space fractional nonlinear Schrödinger equations. (English) Zbl 1499.65451 Int. J. Comput. Math. 99, No. 3, 607-628 (2022). MSC: 65M06 65N06 65M12 35A01 35A02 35Q55 35Q41 26A33 35R11 PDFBibTeX XMLCite \textit{L. Zhai} and \textit{J. Wang}, Int. J. Comput. Math. 99, No. 3, 607--628 (2022; Zbl 1499.65451) Full Text: DOI
Oruç, Ömer A strong-form local meshless approach based on radial basis function-finite difference (RBF-FD) method for solving multi-dimensional coupled damped Schrödinger system appearing in Bose-Einstein condensates. (English) Zbl 07428002 Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 106042, 18 p. (2022). MSC: 65M70 65M06 65N35 65L06 65D12 65D07 65M12 65M15 35Q55 82C10 82M22 PDFBibTeX XMLCite \textit{Ö. Oruç}, Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 106042, 18 p. (2022; Zbl 07428002) Full Text: DOI
Li, Xueyang; Xiao, Aiguo Fourier spectral method on sparse grids for computing ground state of many-particle fractional Schrödinger equations. (English) Zbl 07476649 Int. J. Comput. Math. 98, No. 6, 1218-1232 (2021). MSC: 65-XX 35R11 65F15 65M70 65T50 PDFBibTeX XMLCite \textit{X. Li} and \textit{A. Xiao}, Int. J. Comput. Math. 98, No. 6, 1218--1232 (2021; Zbl 07476649) Full Text: DOI
Kerdboon, J.; Yimnet, S.; Wongsaijai, B.; Mouktonglang, T.; Poochinapan, K. Convergence analysis of the higher-order global mass-preserving numerical method for the symmetric regularized long-wave equation. (English) Zbl 1480.65210 Int. J. Comput. Math. 98, No. 5, 869-902 (2021). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{J. Kerdboon} et al., Int. J. Comput. Math. 98, No. 5, 869--902 (2021; Zbl 1480.65210) Full Text: DOI
Trofimov, Vyacheslav A.; Stepanenko, Svetlana; Razgulin, Alexander Conservation laws of femtosecond pulse propagation described by generalized nonlinear Schrödinger equation with cubic nonlinearity. (English) Zbl 1524.35498 Math. Comput. Simul. 182, 366-396 (2021). MSC: 35Q41 78A60 PDFBibTeX XMLCite \textit{V. A. Trofimov} et al., Math. Comput. Simul. 182, 366--396 (2021; Zbl 1524.35498) Full Text: DOI
Abbaszadeh, Mostafa; Amjadian, Hanieh Second-order finite difference/spectral element formulation for solving the fractional advection-diffusion equation. (English) Zbl 1476.65152 Commun. Appl. Math. Comput. 2, No. 4, 653-669 (2020). MSC: 65L60 65L20 65M70 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{H. Amjadian}, Commun. Appl. Math. Comput. 2, No. 4, 653--669 (2020; Zbl 1476.65152) Full Text: DOI
Chen, Juan; Chen, Fangqi Unconditional \(L_\infty\) convergence of a compact ADI scheme for coupled nonlinear Schrödinger system. (English) Zbl 1437.65092 Appl. Numer. Math. 153, 430-442 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 65M06 65M12 65P10 37K10 35Q55 PDFBibTeX XMLCite \textit{J. Chen} and \textit{F. Chen}, Appl. Numer. Math. 153, 430--442 (2020; Zbl 1437.65092) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi; Zhou, Yong Crank-Nicolson/Galerkin spectral method for solving two-dimensional time-space distributed-order weakly singular integro-partial differential equation. (English) Zbl 1435.65170 J. Comput. Appl. Math. 374, Article ID 112739, 16 p. (2020). MSC: 65M70 65M60 65M06 65M12 65M15 35R09 45K05 33C45 26A33 35R11 PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., J. Comput. Appl. Math. 374, Article ID 112739, 16 p. (2020; Zbl 1435.65170) Full Text: DOI
Ji, Bingquan; Zhang, Luming; Zhou, Xuanxuan Conservative compact difference scheme for the Zakharov-Rubenchik equations. (English) Zbl 1499.65397 Int. J. Comput. Math. 96, No. 3, 537-556 (2019). MSC: 65M06 65N06 35Q51 65M15 35L65 35Q35 PDFBibTeX XMLCite \textit{B. Ji} et al., Int. J. Comput. Math. 96, No. 3, 537--556 (2019; Zbl 1499.65397) Full Text: DOI
Manorot, Panasun; Charoensawan, Phakdi; Dangskul, Supreedee Numerical solutions to the Rosenau-Kawahara equation for shallow water waves via pseudo-compact methods. (English) Zbl 1468.65101 Thai J. Math. 17, No. 2, 571-595 (2019). MSC: 65M06 65M12 86A05 PDFBibTeX XMLCite \textit{P. Manorot} et al., Thai J. Math. 17, No. 2, 571--595 (2019; Zbl 1468.65101) Full Text: Link
Ilati, Mohammad; Dehghan, Mehdi DMLPG method for numerical simulation of soliton collisions in multi-dimensional coupled damped nonlinear Schrödinger system which arises from Bose-Einstein condensates. (English) Zbl 1429.65229 Appl. Math. Comput. 346, 244-253 (2019). MSC: 65M60 35C08 35Q55 35Q82 82C10 PDFBibTeX XMLCite \textit{M. Ilati} and \textit{M. Dehghan}, Appl. Math. Comput. 346, 244--253 (2019; Zbl 1429.65229) Full Text: DOI
Mohebbi, Akbar Crank-Nicolson and Legendre spectral collocation methods for a partial integro-differential equation with a singular kernel. (English) Zbl 1408.65074 J. Comput. Appl. Math. 349, 197-206 (2019). MSC: 65M70 35R09 45K05 65M06 65D32 65M12 PDFBibTeX XMLCite \textit{A. Mohebbi}, J. Comput. Appl. Math. 349, 197--206 (2019; Zbl 1408.65074) Full Text: DOI
Liao, Feng; Zhang, Luming Numerical analysis of a conservative linear compact difference scheme for the coupled Schrödinger-Boussinesq equations. (English) Zbl 1499.65402 Int. J. Comput. Math. 95, No. 5, 961-978 (2018). MSC: 65M06 65N06 35Q55 35Q51 65M12 65M15 35C08 35Q35 PDFBibTeX XMLCite \textit{F. Liao} and \textit{L. Zhang}, Int. J. Comput. Math. 95, No. 5, 961--978 (2018; Zbl 1499.65402) Full Text: DOI
Wang, Jilu Unconditional stability and convergence of Crank-Nicolson Galerkin FEMs for a nonlinear Schrödinger-Helmholtz system. (English) Zbl 1402.65119 Numer. Math. 139, No. 2, 479-503 (2018). Reviewer: Kai Schneider (Marseille) MSC: 65M60 65N30 65N15 65M12 PDFBibTeX XMLCite \textit{J. Wang}, Numer. Math. 139, No. 2, 479--503 (2018; Zbl 1402.65119) Full Text: DOI
Mu, Zhenguo; Li, Haochen; Wang, Yushun A novel energy-preserving scheme for the coupled nonlinear Schrödinger equations. (English) Zbl 1387.65090 Int. J. Comput. Math. 95, No. 1, 61-81 (2018). MSC: 65M06 65M20 65M70 35Q55 PDFBibTeX XMLCite \textit{Z. Mu} et al., Int. J. Comput. Math. 95, No. 1, 61--81 (2018; Zbl 1387.65090) Full Text: DOI
Shi, Dongyang; Wang, Junjun; Yan, Fengna Unconditional superconvergence analysis of an \(H^1\)-Galerkin mixed finite element method for nonlinear Sobolev equations. (English) Zbl 1390.65120 Numer. Methods Partial Differ. Equations 34, No. 1, 145-166 (2018). Reviewer: T. C. Mohan (Chennai) MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{D. Shi} et al., Numer. Methods Partial Differ. Equations 34, No. 1, 145--166 (2018; Zbl 1390.65120) Full Text: DOI
Jiang, Xiaoli; Wang, Xiaofeng A conservation difference scheme of generalized Boussinesq equation. (English) Zbl 1453.65221 Discrete Dyn. Nat. Soc. 2017, Article ID 5392172, 9 p. (2017). MSC: 65M06 65M12 35Q53 PDFBibTeX XMLCite \textit{X. Jiang} and \textit{X. Wang}, Discrete Dyn. Nat. Soc. 2017, Article ID 5392172, 9 p. (2017; Zbl 1453.65221) Full Text: DOI
Hu, Jinsong; Zhou, Jun; Zhuo, Ru A high-accuracy conservative difference approximation for Rosenau-KdV equation. (English) Zbl 1412.65079 J. Nonlinear Sci. Appl. 10, No. 6, 3013-3022 (2017). MSC: 65M06 65N30 PDFBibTeX XMLCite \textit{J. Hu} et al., J. Nonlinear Sci. Appl. 10, No. 6, 3013--3022 (2017; Zbl 1412.65079) Full Text: DOI
Shi, Dongyang; Wang, Junjun Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element. (English) Zbl 1411.65134 Appl. Math. Comput. 305, 1-16 (2017). MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{D. Shi} and \textit{J. Wang}, Appl. Math. Comput. 305, 1--16 (2017; Zbl 1411.65134) Full Text: DOI
Shi, Dongyang; Wang, Junjun Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation. (English) Zbl 1411.65133 Appl. Math. Comput. 294, 216-226 (2017). MSC: 65M60 35K20 35K59 65M12 PDFBibTeX XMLCite \textit{D. Shi} and \textit{J. Wang}, Appl. Math. Comput. 294, 216--226 (2017; Zbl 1411.65133) Full Text: DOI
Shi, Dongyang; Wang, Junjun Unconditional superconvergence analysis of a linearized Galerkin FEM for nonlinear hyperbolic equations. (English) Zbl 1384.65062 Comput. Math. Appl. 74, No. 4, 634-651 (2017). MSC: 65M12 65M60 35L70 65M15 PDFBibTeX XMLCite \textit{D. Shi} and \textit{J. Wang}, Comput. Math. Appl. 74, No. 4, 634--651 (2017; Zbl 1384.65062) Full Text: DOI
Liao, Feng; Zhang, Luming; Wang, Shanshan Numerical analysis of cubic orthogonal spline collocation methods for the coupled Schrödinger-Boussinesq equations. (English) Zbl 1368.65199 Appl. Numer. Math. 119, 194-212 (2017). MSC: 65M70 35Q55 35Q53 65M12 PDFBibTeX XMLCite \textit{F. Liao} et al., Appl. Numer. Math. 119, 194--212 (2017; Zbl 1368.65199) Full Text: DOI
Wang, Huan; Li, Shuguang; Wang, Jue A conservative weighted finite difference scheme for the generalized Rosenau-RLW equation. (English) Zbl 1359.65165 Comput. Appl. Math. 36, No. 1, 63-78 (2017). MSC: 65M06 65M12 65M22 PDFBibTeX XMLCite \textit{H. Wang} et al., Comput. Appl. Math. 36, No. 1, 63--78 (2017; Zbl 1359.65165) Full Text: DOI
Shi, Dongyang; Wang, Junjun; Yan, Fengna Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element. (English) Zbl 1368.65162 J. Sci. Comput. 70, No. 1, 85-111 (2017). Reviewer: Charis Harley (Johannesburg) MSC: 65M12 65M60 35K55 65M15 PDFBibTeX XMLCite \textit{D. Shi} et al., J. Sci. Comput. 70, No. 1, 85--111 (2017; Zbl 1368.65162) Full Text: DOI
Sun, Weiwei; Wang, Jilu Optimal error analysis of Crank-Nicolson schemes for a coupled nonlinear Schrödinger system in 3D. (English) Zbl 1357.65148 J. Comput. Appl. Math. 317, 685-699 (2017). MSC: 65M15 35Q55 65M06 PDFBibTeX XMLCite \textit{W. Sun} and \textit{J. Wang}, J. Comput. Appl. Math. 317, 685--699 (2017; Zbl 1357.65148) Full Text: DOI
Yimnet, S.; Wongsaijai, B.; Rojsiraphisal, T.; Poochinapan, K. Numerical implementation for solving the symmetric regularized long wave equation. (English) Zbl 1410.65334 Appl. Math. Comput. 273, 809-825 (2016). MSC: 65M06 35B25 35Q53 65M12 PDFBibTeX XMLCite \textit{S. Yimnet} et al., Appl. Math. Comput. 273, 809--825 (2016; Zbl 1410.65334) Full Text: DOI
He, Dongdong Exact solitary solution and a three-level linearly implicit conservative finite difference method for the generalized Rosenau-Kawahara-RLW equation with generalized Novikov type perturbation. (English) Zbl 1349.37065 Nonlinear Dyn. 85, No. 1, 479-498 (2016). MSC: 37K10 37K05 35B06 PDFBibTeX XMLCite \textit{D. He}, Nonlinear Dyn. 85, No. 1, 479--498 (2016; Zbl 1349.37065) Full Text: DOI
He, Dongdong New solitary solutions and a conservative numerical method for the Rosenau-Kawahara equation with power law nonlinearity. (English) Zbl 1348.76039 Nonlinear Dyn. 82, No. 3, 1177-1190 (2015). MSC: 76B25 35Q35 PDFBibTeX XMLCite \textit{D. He}, Nonlinear Dyn. 82, No. 3, 1177--1190 (2015; Zbl 1348.76039) Full Text: DOI
Wang, Dongling; Xiao, Aiguo; Yang, Wei Maximum-norm error analysis of a difference scheme for the space fractional CNLS. (English) Zbl 1339.65137 Appl. Math. Comput. 257, 241-251 (2015). MSC: 65M06 35R11 39B12 65M12 65M15 68W25 PDFBibTeX XMLCite \textit{D. Wang} et al., Appl. Math. Comput. 257, 241--251 (2015; Zbl 1339.65137) Full Text: DOI
Ismail, Mohammad S.; Al-Basyouni, Khalil S.; Aydin, Ayhan Conservative finite difference schemes for the chiral nonlinear Schrödinger equation. (English) Zbl 1522.65144 Bound. Value Probl. 2015, Paper No. 89, 14 p. (2015). MSC: 65M06 35C08 35Q41 65M12 PDFBibTeX XMLCite \textit{M. S. Ismail} et al., Bound. Value Probl. 2015, Paper No. 89, 14 p. (2015; Zbl 1522.65144) Full Text: DOI
Kong, Linghua; Hong, Jialin; Ji, Lihai; Zhu, Pengfei Compact and efficient conservative schemes for coupled nonlinear Schrödinger equations. (English) Zbl 1339.65125 Numer. Methods Partial Differ. Equations 31, No. 6, 1814-1843 (2015). Reviewer: Jiguang Sun (Dover) MSC: 65M06 35Q55 65M12 PDFBibTeX XMLCite \textit{L. Kong} et al., Numer. Methods Partial Differ. Equations 31, No. 6, 1814--1843 (2015; Zbl 1339.65125) Full Text: DOI
Wang, Dongling; Xiao, Aiguo; Yang, Wei A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations. (English) Zbl 1349.65339 J. Comput. Phys. 272, 644-655 (2014). MSC: 65M06 35R11 35Q55 PDFBibTeX XMLCite \textit{D. Wang} et al., J. Comput. Phys. 272, 644--655 (2014; Zbl 1349.65339) Full Text: DOI
Wang, Jilu A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation. (English) Zbl 1306.65257 J. Sci. Comput. 60, No. 2, 390-407 (2014). Reviewer: Qin Meng Zhao (Beijing) MSC: 65M15 65M60 35Q55 PDFBibTeX XMLCite \textit{J. Wang}, J. Sci. Comput. 60, No. 2, 390--407 (2014; Zbl 1306.65257) Full Text: DOI
Luo, Yan; Xu, Youcai; Feng, Minfu Conservative difference scheme for generalized Rosenau-KdV equation. (English) Zbl 1291.76231 Adv. Math. Phys. 2014, Article ID 986098, 7 p. (2014). MSC: 76M20 65N06 35Q53 PDFBibTeX XMLCite \textit{Y. Luo} et al., Adv. Math. Phys. 2014, Article ID 986098, 7 p. (2014; Zbl 1291.76231) Full Text: DOI
Hu, Jinsong; Xu, Youcai; Hu, Bing; Xie, Xiaoping Two conservative difference schemes for Rosenau-Kawahara equation. (English) Zbl 1302.65191 Adv. Math. Phys. 2014, Article ID 217393, 11 p. (2014). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{J. Hu} et al., Adv. Math. Phys. 2014, Article ID 217393, 11 p. (2014; Zbl 1302.65191) Full Text: DOI
Hu, Xiuling; Zhang, Luming Conservative compact difference schemes for the coupled nonlinear Schrödinger system. (English) Zbl 1302.65192 Numer. Methods Partial Differ. Equations 30, No. 3, 749-772 (2014). Reviewer: Petr Sváček (Praha) MSC: 65M06 65M12 35Q55 PDFBibTeX XMLCite \textit{X. Hu} and \textit{L. Zhang}, Numer. Methods Partial Differ. Equations 30, No. 3, 749--772 (2014; Zbl 1302.65192) Full Text: DOI
Wang, Dongling; Xiao, Aiguo; Yang, Wei Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative. (English) Zbl 1297.65100 J. Comput. Phys. 242, 670-681 (2013). MSC: 65M06 65M12 35Q55 35R11 PDFBibTeX XMLCite \textit{D. Wang} et al., J. Comput. Phys. 242, 670--681 (2013; Zbl 1297.65100) Full Text: DOI
Pan, Xintian; Zheng, Kelong; Zhang, Luming Finite difference discretization of the Rosenau-RLW equation. (English) Zbl 1290.65079 Appl. Anal. 92, No. 12, 2578-2589 (2013). Reviewer: Fernando Casas (Castellon) MSC: 65M06 35L75 65M12 PDFBibTeX XMLCite \textit{X. Pan} et al., Appl. Anal. 92, No. 12, 2578--2589 (2013; Zbl 1290.65079) Full Text: DOI
Hu, Jinsong; Xu, Youcai; Hu, Bing Conservative linear difference scheme for Rosenau-KdV equation. (English) Zbl 1282.35332 Adv. Math. Phys. 2013, Article ID 423718, 7 p. (2013). MSC: 35Q53 PDFBibTeX XMLCite \textit{J. Hu} et al., Adv. Math. Phys. 2013, Article ID 423718, 7 p. (2013; Zbl 1282.35332) Full Text: DOI
Pan, Xintian; Zhang, Luming Numerical simulation for general rosenau-RLW equation: an average linearized conservative scheme. (English) Zbl 1264.65140 Math. Probl. Eng. 2012, Article ID 517818, 15 p. (2012). MSC: 65M06 35Q53 PDFBibTeX XMLCite \textit{X. Pan} and \textit{L. Zhang}, Math. Probl. Eng. 2012, Article ID 517818, 15 p. (2012; Zbl 1264.65140) Full Text: DOI
Pan, Xintian; Zhang, Luming On the convergence of a conservative numerical scheme for the usual Rosenau-RLW equation. (English) Zbl 1252.65144 Appl. Math. Modelling 36, No. 8, 3371-3378 (2012). MSC: 65M06 35Q53 PDFBibTeX XMLCite \textit{X. Pan} and \textit{L. Zhang}, Appl. Math. Modelling 36, No. 8, 3371--3378 (2012; Zbl 1252.65144) Full Text: DOI
Zuo, Jin-Ming; Zhang, Yao-Ming; Zhang, Tian-De; Chang, Feng A new conservative difference scheme for the general Rosenau-RLW equation. (English) Zbl 1206.65216 Bound. Value Probl. 2010, Article ID 516260, 13 p. (2010). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 65M06 35L75 65M12 PDFBibTeX XMLCite \textit{J.-M. Zuo} et al., Bound. Value Probl. 2010, Article ID 516260, 13 p. (2010; Zbl 1206.65216) Full Text: DOI EuDML