Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
ESAIM: M2AN, 46 4 (2012) 841-874
Published online: 2012-02-03
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Convergence of a quantum lattice Boltzmann scheme to the nonlinear Dirac equation for Gross-Neveu model in 1+1 dimensions
Ningning Li, Jing Zhang and Yongqian ZhangActa Mathematica Scientia 44 (6) 2249 (2024)
https://doi.org/10.1007/s10473-024-0611-3
Uniformly Accurate Nested Picard Iterative Integrators for the Nonlinear Dirac Equation in the Nonrelativistic Regime
Yongyong Cai and Yan WangMultiscale Modeling & Simulation 20 (1) 164 (2022)
https://doi.org/10.1137/20M133573X
Energy-preserving exponential integrator Fourier pseudo-spectral schemes for the nonlinear Dirac equation
Jiyong LiApplied Numerical Mathematics 172 1 (2022)
https://doi.org/10.1016/j.apnum.2021.09.006
Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential
Weizhu Bao, Yongyong Cai and Jia YinSIAM Journal on Numerical Analysis 59 (2) 1040 (2021)
https://doi.org/10.1137/19M1271828
Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation
Jiyong Li and Tingchun WangApplied Numerical Mathematics 162 150 (2021)
https://doi.org/10.1016/j.apnum.2020.12.010
Initial boundary value problem for nonlinear Dirac equation of Gross-Neveu type in 1 + 1 dimensions
Yongqian Zhang and Qin ZhaoJournal of Mathematical Analysis and Applications 477 (1) 708 (2019)
https://doi.org/10.1016/j.jmaa.2019.04.058
Large Time Behavior of Solution to Nonlinear Dirac Equation in 1+1 Dimensions
Yongqian Zhang and Qin ZhaoActa Mathematica Scientia 39 (2) 597 (2019)
https://doi.org/10.1007/s10473-019-0221-7
A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime
Yongyong Cai and Yan WangESAIM: Mathematical Modelling and Numerical Analysis 52 (2) 543 (2018)
https://doi.org/10.1051/m2an/2018015
Lax Pair and new exact solutions of the nonlinear Dirac equation
Y.H. Sabbah, U. Al Khawaja and P.S. VinayagamCommunications in Nonlinear Science and Numerical Simulation 61 167 (2018)
https://doi.org/10.1016/j.cnsns.2018.02.009
Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime
WeiZhu Bao, YongYong Cai, XiaoWei Jia and Jia YinScience China Mathematics 59 (8) 1461 (2016)
https://doi.org/10.1007/s11425-016-0272-y
Global solution to nonlinear Dirac equation for Gross–Neveu model in 1+1 dimensions
Yongqian Zhang and Qin ZhaoNonlinear Analysis: Theory, Methods & Applications 118 82 (2015)
https://doi.org/10.1016/j.na.2015.02.007
A well-balanced and asymptotic-preserving scheme for the one-dimensional linear Dirac equation
Laurent GosseBIT Numerical Mathematics 55 (2) 433 (2015)
https://doi.org/10.1007/s10543-014-0510-4
Numerical methods for nonlinear Dirac equation
Jian Xu, Sihong Shao and Huazhong TangJournal of Computational Physics 245 131 (2013)
https://doi.org/10.1016/j.jcp.2013.03.031