1 |
W. Bao and C. Su, Uniform error estimates of a finite difference method for the Klein-Gordon-Schrodinger system in the nonrelativistic and massless limit regimes, Kinetic and Related Models, 11 (2018), 1037-1062.
DOI
|
2 |
J. Cai, J. Hong and Y.Wang, Local energy and momentum-preserving schemes for Klein-Gordon-Schrodinger equations and convergence analysis, Numerical Methods for Partial Differential Equations, 33 (2017), 1329-1351.
DOI
|
3 |
L. Kong, M. Chen and X. Yin, A novel kind of efficient symplectic scheme for Klein-Gordon-Schrodinger equation, Applied Numerical Mathematics, 135 (2019), 481-496.
DOI
|
4 |
T. Wang, X. Zhao and J. Jiang, Unconditional and optimal -error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrodinger equation in high dimensions, Advances in Computational Mathematics, 44 (2018), 477-503.
DOI
|
5 |
W. Bao and L. Yang, Efficient and accurate numerical methods for the Klein-Gordon-Schrodinger equations, Journal of Computational Physics, 225 (2007), 1863-1893.
DOI
|
6 |
W. Bao and X. Zhao, A uniformly accurate multiscale time integrator Fourier pseudospectral method for the Klein-Gordon-Schrodinger equations in the nonrelativistic limit regime, Numerische Mathematik, 135 (2017), 833-873.
DOI
|
7 |
M. Dehghan and A. Taleei, Numerical solution of the Yukawa-coupled Klein-Gordon-Schrodinger equations via a Chebyshev pseudospectral multidomain method, Applied Mathematical Modelling, 36 (2012), 2340-2349.
DOI
|
8 |
Q. Hong, Y. Wang and J. Wang, Optimal error estimate of a linear Fourier pseudo-spectral scheme for two dimensional Klein-Gordon-Schrodinger equations, Journal of Mathematical Analysis and Applications, 468 (2018), 817-838.
DOI
|
9 |
L. Kong, J. Zhang, Y. Cao, Y. Duan and H. Huang, Semi-explicit symplectic partitioned Runge-Kutta Fourier pseudo-spectral scheme for Klein-Gordon-Schrodinger equations, Computer Physics Communications, 181 (2010), 1369-1377.
DOI
|
10 |
H. Liang, Linearly implicit conservative schemes for long-term numerical simulation of Klein-Gordon-Schrodinger equations, Applied Mathematics and Computation, 238 (2014), 475-484.
DOI
|
11 |
J. Wang, Y. Wang and D. Liang, Analysis of a Fourier pseudo-spectral conservative scheme for the Klein-Gordon-Schrodinger equation, International Journal of Computer Mathematics, 95 (2018), 36-60.
DOI
|
12 |
J. Hong, S. Jiang and C. Li, Explicit multi-symplectic methods for Klein-Gordon-Schrodinger equations, Journal of Computational Physics, 228 (2009), 3517-3532.
DOI
|
13 |
J. Zhang and L. Kong, New energy-preserving schemes for Klein-Gordon-Schrodinger equations, Applied Mathematical Modelling, 40 (2016), 6969-6982.
DOI
|
14 |
M. Dehghan and V. Mohammadi, Two numerical meshless techniques based on radial basis functions (RBFs) and the method of generalized moving least squares (GMLS) for simulation of coupled Klein-Gordon-Schrodinger (KGS) equations, Computer and Mathematics with Applications, 71 (2016), 892-921.
DOI
|
15 |
J. Yan and C.-W. Shu, A local discontinuous Galerkin method for KdV-type equations, SIAM Journal on Numerical Analysis, 40 (2002), 769-791.
DOI
|
16 |
S. Wang and L. Zhang, A class of conservative orthogonal spline collocation schemes for solving coupled Klein-Gordon-Schrodinger equations, Applied Mathematics and Computation, 203 (2008), 799-812.
DOI
|
17 |
H. Yang, Error estimates for a class of energy- and Hamiltonian-preserving local discontinuous Galerkin methods for the Klein-Gordon-Schrodinger equations, Journal of Applied Mathematics and Computing, 62 (2020), 377-424.
DOI
|
18 |
B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM Journal on Numerical Analysis, 35 (1998), 2440-2463.
DOI
|
19 |
J. Yan and C.-W. Shu, Local discontinuous Galerkin methods for partial differential equations with higher order Derivatives, Journal of Scientific Computing, 17 (2002), 27-47.
DOI
|
20 |
C.-S. Chou, W. Sun, Y. Xing and H. Yang, Local discontinuous Galerkin methods for the Khokhlov-Zabolotskaya-Kuznetzov equation, Journal of Scientific Computing, 73 (2017), 593-616.
DOI
|
21 |
Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations, Physica D, 208 (2005), 21-58.
DOI
|
22 |
Y. Xing, C.-S. Chou and C.-W. Shu, Energy conserving local discontinuous Galerkin methods for wave propagation problems, Inverse Problems and Imaging, 7 (2013), 967-986.
DOI
|
23 |
R. Zhang, X. Yu, M. Li and X. Li, A conservative local discontinuous Galerkin method for the solution of nonlinear Schrodinger equation in two dimensions, Science China Mathematics, 60 (2017), 2515-2530.
DOI
|
24 |
H. Yang, F. Li and J. Qiu, Dispersion and dissipation errors of two fully discrete discontinuous Galerkin methods, Journal of Scientific Computing, 55 (2013), 552-574.
DOI
|
25 |
H. Yang, High-order energy and linear momentum conserving methods for the Klein-Gordon equation, Mathematics, 6 (2018), 200.
DOI
|
26 |
H. Yang and F. Li, Error estimates of Runge-Kutta discontinuous Galerkin methods for the Vlasov-Maxwell system, ESAIM: Mathematical Modelling and Numerical Analysis, 49 (2015), 69-99.
DOI
|