Open Access
| Issue |
ESAIM: M2AN
Volume 57, Number 6, November-December 2023
|
|
|---|---|---|
| Page(s) | 3483 - 3498 | |
| DOI | https://doi.org/10.1051/m2an/2023087 | |
| Published online | 20 December 2023 | |
- P. Bader, S. Blanes, F. Casas and N. Kopylov, Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass. J. Comput. Appl. Math. 350 (2019) 130–138. [CrossRef] [MathSciNet] [Google Scholar]
- W. Bao and X. Dong, Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime. Numer. Math. 120 (2012) 189–229. [Google Scholar]
- S. Blanes, F. Casas, J.A. Oteo and J. Ros, The Magnus expansion and some of its applications. Phys. Rep. 470 (2009) 151–238. [CrossRef] [MathSciNet] [Google Scholar]
- J.-B. Chen and H. Liu, Multisymplectic pseudospectral discretizations for (3 + 1)-dimensional Klein-Gordon equation. Commun. Theor. Phys. (Beijing) 50 (2008) 1052–1054. [CrossRef] [MathSciNet] [Google Scholar]
- D. Cohen, E. Hairer and C. Lubich, Modulated Fourier expansions of highly oscillatory differential equations. Found. Comput. Math. 3 (2003) 327–345. [CrossRef] [MathSciNet] [Google Scholar]
- M. Condon, K. Kropielnicka, K. Lademann and R. Perczyński, Asymptotic numerical solver for the linear Klein-Gordon equation with space- and time-dependent mass. Appl. Math. Lett. 115 (2021) 106935. [CrossRef] [Google Scholar]
- E. Faou and K. Schratz, Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime. Numer. Math. 126 (2014) 441–469. [CrossRef] [MathSciNet] [Google Scholar]
- J. Gao and A. Iserles, Error analysis of the extended filon-type method for highly oscillatory integrals. Res. Math. Sci. 4 (2017). [Google Scholar]
- M. Hochbruck and C. Lubich, A gautschi-type method for oscillatory second-order differential equations. Numer. Math. 83 (1998). [Google Scholar]
- S. Ikram, S. Saleem and M.Z. Hussain, Approximations to linear Klein-Gordon equations using haar wavelet. Ain Shams Eng. J. (2021). [Google Scholar]
- A. Iserles and S.P. Nørsett, Efficient quadrature of highly oscillatory integrals using derivatives. Proc. R. Soc. A Math. Phys. Eng. Sci. 461 (2005) 1383–1399. [Google Scholar]
- N. Kasron, E.S. Suharto, R.F. Deraman, K.I. Othman and M.A.S. Nasir, Numerical solution of linear Klein-Gordon equation using FDAM scheme. In Proceedings of the International Conference on Education, Mathematics and Science 2016 (ICEMS2016) in Conjunction with 4th International Postgraduate Conference on Science and Mathematics 2016 (IPCSM2016), Vol. 1847 of American Institute of Physics Conference Series (2017) 020021. [Google Scholar]
- L. Kofman, A.D. Linde and A.A. Starobinsky, Reheating after inflation. Phys. Rev. Lett. 73 (1994) 3195–3198. [CrossRef] [PubMed] [Google Scholar]
- D.A. Kopriva, Implementing Spectral Methods for Partial Differential Equations. Scientific Computation. Algorithms for scientists and engineers. Springer, Berlin (2009). [Google Scholar]
- K. Kropielnicka, K. Lademann and K. Schratz, Effective highly accurate integrators for linear Klein-Gordon equations from low to high frequency regimes. Preprint arXiv:2112.08908 (2022). [Google Scholar]
- K. Lademann, Bridge of knowledge – Gdansk University of Technology, https://mostwiedzy.pl/pl/karolina-lademann,1385645-1/programy (2023) [Google Scholar]
- A. Mostafazadeh, Hilbert space structures on the solution space of klein-gordon-type evolution equations. Class. Quantum Gravity 20 (2003) 155–171. [CrossRef] [Google Scholar]
- A. Mostafazadeh, Quantum mechanics of Klein-Gordon-type fields and quantum cosmology. Ann. Phys. 309 (2004) 1–48. [CrossRef] [Google Scholar]
- A.S.V. Ravi Kanth and K. Aruna, Differential transform method for solving the linear and nonlinear klein–gordon equation. Comput. Phys. Commun. 180 (2009) 708–711. [CrossRef] [Google Scholar]
- F. Shakeri and M. Dehghan, Numerical solution of the Klein-Gordon equation via He’s variational iteration method. Nonlinear Dynam. 51 (2008) 89–97. [Google Scholar]
- E. Yusufoğlu, The variational iteration method for studying the Klein-Gordon equation. Appl. Math. Lett. 21 (2008) 669–674. [CrossRef] [MathSciNet] [Google Scholar]
- M. Znojil, Quantization of big bang in crypto-hermitian heisenberg picture. Springer Proc. Phys. 184 (2016) 383–399. [CrossRef] [Google Scholar]
- M. Znojil, Non-Hermitian interaction representation and its use in relativistic quantum mechanics. Ann. Phys. 385 (2017) 162–179. [CrossRef] [Google Scholar]
- M. Znojil, Klein-Gordon equation with the time- and space-dependent mass: Unitary evolution picture. Ann. Phys. 385 (2017) 162. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.