Wang, Jialing; Wang, Tingchun; Wang, Yushun A new framework of convergence analysis for solving the general nonlinear Schrödinger equation using the Fourier pseudo-spectral method in two dimensions. (English) Zbl 07679220 Adv. Appl. Math. Mech. 15, No. 3, 786-813 (2023). MSC: 65Mxx 35Q55 65T50 PDFBibTeX XMLCite \textit{J. Wang} et al., Adv. Appl. Math. Mech. 15, No. 3, 786--813 (2023; Zbl 07679220) Full Text: DOI
Liu, Jianfeng; Wang, Tingchun; Zhang, Teng A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation. (English) Zbl 1506.65127 Numer. Algorithms 92, No. 2, 1153-1182 (2023). MSC: 65M06 65N06 65M12 65M15 35R11 35Q41 35Q55 PDFBibTeX XMLCite \textit{J. Liu} et al., Numer. Algorithms 92, No. 2, 1153--1182 (2023; Zbl 1506.65127) Full Text: DOI
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 PDFBibTeX XMLCite \textit{S. Li} et al., Int. J. Comput. Math. 98, No. 2, 340--356 (2021; Zbl 1480.65285) Full Text: DOI
Cheng, Yue; Wang, Tingchun; Guo, Boling An efficient and unconditionally convergent Galerkin finite element method for the nonlinear Schrödinger equation in high dimensions. (English) Zbl 1488.65412 Adv. Appl. Math. Mech. 13, No. 4, 735-760 (2021). MSC: 65M60 35Q55 35Q41 41A58 65N30 65M12 65M15 PDFBibTeX XMLCite \textit{Y. Cheng} et al., Adv. Appl. Math. Mech. 13, No. 4, 735--760 (2021; Zbl 1488.65412) Full Text: DOI
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 PDFBibTeX XMLCite \textit{J. Li} and \textit{T. Wang}, Appl. Numer. Math. 162, 150--170 (2021; Zbl 1457.81035) Full Text: DOI
Wang, Tingchun; Wang, Jialing; Guo, Boling Two completely explicit and unconditionally convergent Fourier pseudo-spectral methods for solving the nonlinear Schrödinger equation. (English) Zbl 1453.65366 J. Comput. Phys. 404, Article ID 109116, 21 p. (2020). MSC: 65M70 65M12 65M15 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., J. Comput. Phys. 404, Article ID 109116, 21 p. (2020; Zbl 1453.65366) Full Text: DOI
Xue, Xiang; Wang, Tingchun A new compact finite difference scheme for the quintic nonlinear Schrödinger equation. (A new compact finite difference scheme for the quantic nonlinear Schrödinger equation.) (Chinese. English summary) Zbl 1449.65206 J. Math., Wuhan Univ. 39, No. 4, 555-565 (2019). MSC: 65M06 65M15 35Q55 PDFBibTeX XMLCite \textit{X. Xue} and \textit{T. Wang}, J. Math., Wuhan Univ. 39, No. 4, 555--565 (2019; Zbl 1449.65206) Full Text: DOI
Wang, Tingchun; Guo, Boling Unconditional convergence of linearized implicit finite difference method for the 2D/3D Gross-Pitaevskii equation with angular momentum rotation. (English) Zbl 1426.65132 Sci. China, Math. 62, No. 9, 1669-1686 (2019). MSC: 65M06 65M12 65M15 35Q55 PDFBibTeX XMLCite \textit{T. Wang} and \textit{B. Guo}, Sci. China, Math. 62, No. 9, 1669--1686 (2019; Zbl 1426.65132) Full Text: DOI
Wang, Tingchun; Zhang, Wen; Wang, Guodong Compact finite difference schemes for the dissipative nonlinear Schrödinger equation. (Chinese. English summary) Zbl 1438.65195 Chin. J. Eng. Math. 35, No. 6, 693-706 (2018). MSC: 65M06 65M15 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., Chin. J. Eng. Math. 35, No. 6, 693--706 (2018; Zbl 1438.65195) Full Text: DOI
Wang, Ting-Chun; Zhang, Wen; Zhu, Chen-Yi Conservation laws and error estimates of several classical finite difference schemes for the nonlinear Schrödinger/Gross-Pitaevskii equation. (English) Zbl 1407.65133 Methods Appl. Anal. 25, No. 2, 97-116 (2019). MSC: 65M06 65M12 35Q55 65M15 PDFBibTeX XMLCite \textit{T.-C. Wang} et al., Methods Appl. Anal. 25, No. 2, 97--116 (2018; Zbl 1407.65133) Full Text: DOI
Wang, Tingchun; Zhao, Xiaofei Unconditional \(L^{\infty }\)-convergence of two compact conservative finite difference schemes for the nonlinear Schrödinger equation in multi-dimensions. (English) Zbl 1404.65103 Calcolo 55, No. 3, Paper No. 34, 26 p. (2018). MSC: 65M06 65M12 35Q55 65M15 PDFBibTeX XMLCite \textit{T. Wang} and \textit{X. Zhao}, Calcolo 55, No. 3, Paper No. 34, 26 p. (2018; Zbl 1404.65103) Full Text: DOI
Wang, Tingchun; Zhao, Xiaofei; Jiang, Jiaping Unconditional and optimal \(H^2\)-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions. (English) Zbl 1448.65122 Adv. Comput. Math. 44, No. 2, 477-503 (2018). MSC: 65M06 65M12 35Q53 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., Adv. Comput. Math. 44, No. 2, 477--503 (2018; Zbl 1448.65122) Full Text: DOI
Wang, Tingchun; Jiang, Jiaping; Xue, Xiang Unconditional and optimal \(H^{1}\) error estimate of a Crank-Nicolson finite difference scheme for the Gross-Pitaevskii equation with an angular momentum rotation term. (English) Zbl 1379.65066 J. Math. Anal. Appl. 459, No. 2, 945-958 (2018). MSC: 65M06 65M15 65M12 35Q76 35Q82 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., J. Math. Anal. Appl. 459, No. 2, 945--958 (2018; Zbl 1379.65066) Full Text: DOI
Wang, Tingchun; Wang, Guodong; Zhang, Wen; He, Ningxia An unconditionally convergent and linearized compact finite difference scheme for the nonlinear Schrödinger equation with a dissipative term. (Chinese. English summary) Zbl 1399.65172 Acta Math. Appl. Sin. 40, No. 1, 1-15 (2017). MSC: 65M06 65M15 35Q55 65M12 PDFBibTeX XMLCite \textit{T. Wang} et al., Acta Math. Appl. Sin. 40, No. 1, 1--15 (2017; Zbl 1399.65172)
Hong, Jialin; Ji, Lihai; Kong, Linghua; Wang, Tingchun Optimal error estimate of a compact scheme for nonlinear Schrödinger equation. (English) Zbl 1370.65072 Appl. Numer. Math. 120, 68-81 (2017). MSC: 65P10 35Q55 37K10 37M15 65M15 65M12 PDFBibTeX XMLCite \textit{J. Hong} et al., Appl. Numer. Math. 120, 68--81 (2017; Zbl 1370.65072) Full Text: DOI
Wang, Tingchun A linearized, decoupled, and energy-preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations. (English) Zbl 1371.65088 Numer. Methods Partial Differ. Equations 33, No. 3, 840-867 (2017). Reviewer: Ivan Secrieru (Chişinău) MSC: 65M06 35Q55 65M12 65M15 PDFBibTeX XMLCite \textit{T. Wang}, Numer. Methods Partial Differ. Equations 33, No. 3, 840--867 (2017; Zbl 1371.65088) Full Text: DOI
Wang, Tingchun Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator. (English) Zbl 1300.65061 J. Math. Anal. Appl. 422, No. 1, 286-308 (2015). MSC: 65M06 35Q55 65M12 65M15 PDFBibTeX XMLCite \textit{T. Wang}, J. Math. Anal. Appl. 422, No. 1, 286--308 (2015; Zbl 1300.65061) Full Text: DOI
Wang, Tingchun Optimal point-wise error estimate of a compact difference scheme for the Klein-Gordon-Schrödinger equation. (English) Zbl 1308.65147 J. Math. Anal. Appl. 412, No. 1, 155-167 (2014). MSC: 65M06 65M12 35Q55 PDFBibTeX XMLCite \textit{T. Wang}, J. Math. Anal. Appl. 412, No. 1, 155--167 (2014; Zbl 1308.65147) Full Text: DOI
Wang, Tingchun Optimal point-wise error estimate of a compact finite difference scheme for a coupled nonlinear Schrödinger equation. (English) Zbl 1313.65228 J. Comput. Math. 32, No. 1, 58-74 (2014). MSC: 65M06 65M15 35Q55 65M12 PDFBibTeX XMLCite \textit{T. Wang}, J. Comput. Math. 32, No. 1, 58--74 (2014; Zbl 1313.65228) Full Text: DOI
Wang, Tingchun; Guo, Boling; Xu, Qiubin Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions. (English) Zbl 1349.65347 J. Comput. Phys. 243, 382-399 (2013). MSC: 65M06 35Q55 65M12 PDFBibTeX XMLCite \textit{T. Wang} et al., J. Comput. Phys. 243, 382--399 (2013; Zbl 1349.65347) Full Text: DOI
Wang, Shanshan; Wang, Tingchun; Zhang, Luming Numerical computations for \(N\)-coupled nonlinear Schrödinger equations by split step spectral methods. (English) Zbl 1329.65239 Appl. Math. Comput. 222, 438-452 (2013). MSC: 65M70 35Q55 PDFBibTeX XMLCite \textit{S. Wang} et al., Appl. Math. Comput. 222, 438--452 (2013; Zbl 1329.65239) Full Text: DOI
Wang, Tingchun A linearized compact difference scheme for the nonlinear Schrödinger equation. (Chinese. English summary) Zbl 1289.65194 J. Nanjing Univ. Inf. Sci. Technol., Nat. Sci. 4, No. 6, 569-572 (2012). MSC: 65M06 65M12 35Q55 PDFBibTeX XMLCite \textit{T. Wang}, J. Nanjing Univ. Inf. Sci. Technol., Nat. Sci. 4, No. 6, 569--572 (2012; Zbl 1289.65194)
Wang, Tingchun A linearized compact difference scheme for solving the nonlinear Schrödinger equation. (Chinese. English summary) Zbl 1289.65193 J. Numer. Methods Comput. Appl. 33, No. 4, 312-320 (2012). MSC: 65M06 65M12 35Q55 PDFBibTeX XMLCite \textit{T. Wang}, J. Numer. Methods Comput. Appl. 33, No. 4, 312--320 (2012; Zbl 1289.65193)
Wang, Tingchun Convergence of an eighth-order compact difference scheme for the nonlinear Schrödinger equation. (English) Zbl 1268.65119 Adv. Numer. Anal. 2012, Article ID 913429, 24 p. (2012). MSC: 65M06 35Q55 65M12 65H10 PDFBibTeX XMLCite \textit{T. Wang}, Adv. Numer. Anal. 2012, Article ID 913429, 24 p. (2012; Zbl 1268.65119) Full Text: DOI
Wang, Tingchun; Guo, Boling Unconditional convergence of two conservative compact difference schemes for nonlinear Schrödinger equation in one dimension. (Chinese. English summary) Zbl 1488.65296 Sci. Sin., Math. 41, No. 3, 207-233 (2011). MSC: 65M06 65M12 65B05 35Q55 PDFBibTeX XMLCite \textit{T. Wang} and \textit{B. Guo}, Sci. Sin., Math. 41, No. 3, 207--233 (2011; Zbl 1488.65296) Full Text: DOI
Wang, Tingchun Maximum norm error bound of a linearized difference scheme for a coupled nonlinear Schrödinger equations. (English) Zbl 1227.65086 J. Comput. Appl. Math. 235, No. 14, 4237-4250 (2011). Reviewer: Vit Dolejsi (Praha) MSC: 65M15 65M06 65M12 35Q55 PDFBibTeX XMLCite \textit{T. Wang}, J. Comput. Appl. Math. 235, No. 14, 4237--4250 (2011; Zbl 1227.65086) Full Text: DOI
Wang, Tingchun; Zhang, Luming; Chen, Fangqi On Sonnier-Christov’s difference scheme for the nonlinear coupled Schrödinger system. (Chinese. English summary) Zbl 1224.65215 Acta Math. Sci., Ser. A, Chin. Ed. 30, No. 1, 114-125 (2010). MSC: 65M06 65M12 65M15 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., Acta Math. Sci., Ser. A, Chin. Ed. 30, No. 1, 114--125 (2010; Zbl 1224.65215)
Wang, Tingchun; Guo, Boling; Zhang, Luming New conservative difference schemes for a coupled nonlinear Schrödinger system. (English) Zbl 1205.65242 Appl. Math. Comput. 217, No. 4, 1604-1619 (2010). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65M06 35Q55 65M12 65Y05 PDFBibTeX XMLCite \textit{T. Wang} et al., Appl. Math. Comput. 217, No. 4, 1604--1619 (2010; Zbl 1205.65242) Full Text: DOI
Wang, Tingchun; Nie, Tao; Zhang, Luming Analysis of a symplectic difference scheme for a coupled nonlinear Schrödinger system. (English) Zbl 1172.65049 J. Comput. Appl. Math. 231, No. 2, 745-759 (2009). Reviewer: Norikazu Saito (Tokyo) MSC: 65M06 65M12 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., J. Comput. Appl. Math. 231, No. 2, 745--759 (2009; Zbl 1172.65049) Full Text: DOI
Wang, Tingchun; Zhang, Luming; Chen, Fangqi Numerical analysis of a multi-symplectic scheme for a strongly coupled Schrödinger system. (English) Zbl 1158.65086 Appl. Math. Comput. 203, No. 1, 413-431 (2008). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65P10 37M15 37K05 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., Appl. Math. Comput. 203, No. 1, 413--431 (2008; Zbl 1158.65086) Full Text: DOI
Wang, Tingchun; Nie, Tao; Zhang, Luming; Chen, Fangqi Numerical simulation of a nonlinearly coupled Schrödinger system: A linearly uncoupled finite difference scheme. (English) Zbl 1202.65116 Math. Comput. Simul. 79, No. 3, 607-621 (2008). Reviewer: Snezhana Gocheva-Ilieva (Plovdiv) MSC: 65M06 65M12 35Q55 35Q51 PDFBibTeX XMLCite \textit{T. Wang} et al., Math. Comput. Simul. 79, No. 3, 607--621 (2008; Zbl 1202.65116) Full Text: DOI
Wang, Tingchun; Zhang, Luming; Chen, Fangqi; Nie, Tao; Liu, Xueyi Convergence analysis of a new difference method for Klein-Gordon-Schrödinger equations. (Chinese. English summary) Zbl 1164.65030 Appl. Math., Ser. A (Chin. Ed.) 23, No. 1, 41-48 (2008). MSC: 65M06 65M12 65M15 65Y05 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., Appl. Math., Ser. A (Chin. Ed.) 23, No. 1, 41--48 (2008; Zbl 1164.65030)
Wang, Tingchun; Zhang, Luming; Chen, Fangqi Conservative difference scheme based on numerical analysis for nonlinear Schrödinger equation with wave operator. (English) Zbl 1111.65076 Trans. Nanjing Univ. Aeronaut. Astronaut. 23, No. 2, 87-93 (2006). MSC: 65M06 65M12 65M15 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., Trans. Nanjing Univ. Aeronaut. Astronaut. 23, No. 2, 87--93 (2006; Zbl 1111.65076)