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Higher-order accurate Runge-Kutta discontinuous Galerkin methods for a nonlinear Dirac model
1. | LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China, China |
[1] |
Da Xu. Numerical solutions of viscoelastic bending wave equations with two term time kernels by Runge-Kutta convolution quadrature. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2389-2416. doi: 10.3934/dcdsb.2017122 |
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Elisa Giesecke, Axel Kröner. Classification with Runge-Kutta networks and feature space augmentation. Journal of Computational Dynamics, 2021, 8 (4) : 495-520. doi: 10.3934/jcd.2021018 |
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Yinhua Xia, Yan Xu, Chi-Wang Shu. Efficient time discretization for local discontinuous Galerkin methods. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 677-693. doi: 10.3934/dcdsb.2007.8.677 |
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Blanca Ayuso, José A. Carrillo, Chi-Wang Shu. Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system. Kinetic and Related Models, 2011, 4 (4) : 955-989. doi: 10.3934/krm.2011.4.955 |
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Maria J. Esteban, Eric Séré. An overview on linear and nonlinear Dirac equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 381-397. doi: 10.3934/dcds.2002.8.381 |
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Thomas Bartsch, Tian Xu. Strongly localized semiclassical states for nonlinear Dirac equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 29-60. doi: 10.3934/dcds.2020297 |
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Xu Zhang. On the concentration of semiclassical states for nonlinear Dirac equations. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5389-5413. doi: 10.3934/dcds.2018238 |
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Yu Chen, Yanheng Ding, Tian Xu. Potential well and multiplicity of solutions for nonlinear Dirac equations. Communications on Pure and Applied Analysis, 2020, 19 (1) : 587-607. doi: 10.3934/cpaa.2020028 |
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Antonia Katzouraki, Tania Stathaki. Intelligent traffic control on internet-like topologies - integration of graph principles to the classic Runge--Kutta method. Conference Publications, 2009, 2009 (Special) : 404-415. doi: 10.3934/proc.2009.2009.404 |
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Wenjuan Zhai, Bingzhen Chen. A fourth order implicit symmetric and symplectic exponentially fitted Runge-Kutta-Nyström method for solving oscillatory problems. Numerical Algebra, Control and Optimization, 2019, 9 (1) : 71-84. doi: 10.3934/naco.2019006 |
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Xiaomeng Li, Qiang Xu, Ailing Zhu. Weak Galerkin mixed finite element methods for parabolic equations with memory. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 513-531. doi: 10.3934/dcdss.2019034 |
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Jiwei Jia, Young-Ju Lee, Yue Feng, Zichan Wang, Zhongshu Zhao. Hybridized weak Galerkin finite element methods for Brinkman equations. Electronic Research Archive, 2021, 29 (3) : 2489-2516. doi: 10.3934/era.2020126 |
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Mahboub Baccouch. Superconvergence of the semi-discrete local discontinuous Galerkin method for nonlinear KdV-type problems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (1) : 19-54. doi: 10.3934/dcdsb.2018104 |
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Andreas C. Aristotelous, Ohannes Karakashian, Steven M. Wise. A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn-Hilliard equation and an efficient nonlinear multigrid solver. Discrete and Continuous Dynamical Systems - B, 2013, 18 (9) : 2211-2238. doi: 10.3934/dcdsb.2013.18.2211 |
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Yin Yang, Yunqing Huang. Spectral Jacobi-Galerkin methods and iterated methods for Fredholm integral equations of the second kind with weakly singular kernel. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 685-702. doi: 10.3934/dcdss.2019043 |
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