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Conservative numerical scheme in complex arithmetic for coupled nonlinear Schrödinger equations
1. | Department of Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1000 Sofia, Bulgaria |
2. | Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States |
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Gianluca Frasca-Caccia, Peter E. Hydon. Locally conservative finite difference schemes for the modified KdV equation. Journal of Computational Dynamics, 2019, 6 (2) : 307-323. doi: 10.3934/jcd.2019015 |
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Guoliang Zhang, Shaoqin Zheng, Tao Xiong. A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations. Electronic Research Archive, 2021, 29 (1) : 1819-1839. doi: 10.3934/era.2020093 |
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Claire david@lmm.jussieu.fr David, Pierre Sagaut. Theoretical optimization of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 286-293. doi: 10.3934/proc.2007.2007.286 |
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Zalman Balanov, Carlos García-Azpeitia, Wieslaw Krawcewicz. On variational and topological methods in nonlinear difference equations. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2813-2844. doi: 10.3934/cpaa.2018133 |
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Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 1503-1528. doi: 10.3934/era.2020079 |
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Emma Hoarau, Claire david@lmm.jussieu.fr David, Pierre Sagaut, Thiên-Hiêp Lê. Lie group study of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 495-505. doi: 10.3934/proc.2007.2007.495 |
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Xiaozhong Yang, Xinlong Liu. Numerical analysis of two new finite difference methods for time-fractional telegraph equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3921-3942. doi: 10.3934/dcdsb.2020269 |
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Z. Jackiewicz, B. Zubik-Kowal, B. Basse. Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics. Mathematical Biosciences & Engineering, 2009, 6 (3) : 561-572. doi: 10.3934/mbe.2009.6.561 |
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Patrick Henning, Johan Wärnegård. Numerical comparison of mass-conservative schemes for the Gross-Pitaevskii equation. Kinetic and Related Models, 2019, 12 (6) : 1247-1271. doi: 10.3934/krm.2019048 |
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Ya-Xiang Yuan. Recent advances in numerical methods for nonlinear equations and nonlinear least squares. Numerical Algebra, Control and Optimization, 2011, 1 (1) : 15-34. doi: 10.3934/naco.2011.1.15 |
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Roumen Anguelov, Jean M.-S. Lubuma, Meir Shillor. Dynamically consistent nonstandard finite difference schemes for continuous dynamical systems. Conference Publications, 2009, 2009 (Special) : 34-43. doi: 10.3934/proc.2009.2009.34 |
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Walid K. Abou Salem, Xiao Liu, Catherine Sulem. Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1637-1649. doi: 10.3934/dcds.2011.29.1637 |
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Adam M. Oberman. Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 221-238. doi: 10.3934/dcdsb.2008.10.221 |
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Bernard Ducomet, Alexander Zlotnik, Ilya Zlotnik. On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation. Kinetic and Related Models, 2009, 2 (1) : 151-179. doi: 10.3934/krm.2009.2.151 |
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Lih-Ing W. Roeger. Dynamically consistent discrete Lotka-Volterra competition models derived from nonstandard finite-difference schemes. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 415-429. doi: 10.3934/dcdsb.2008.9.415 |
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Takahiro Hashimoto. Nonexistence of global solutions of nonlinear Schrodinger equations in non star-shaped domains. Conference Publications, 2007, 2007 (Special) : 487-494. doi: 10.3934/proc.2007.2007.487 |
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