TY - JOUR
T1 - High-order energy and linear momentum conserving methods for the Klein-Gordon equation
AU - Yang, He
N1 - Funding Information:
Acknowledgments: The author acknowledges the support from Augusta University. The author would also like to thank three anonymous reviewers for their insightful and constructive comments, which help to improve the quality of this paper.
Publisher Copyright:
© 2018 by the author.
PY - 2018/10/12
Y1 - 2018/10/12
N2 - The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and linear momentum of the equation have not been considered. In this paper, we propose high-order numerical methods to solve the Klein-Gordon equation, present the energy and linear momentum conservation properties of our numerical schemes, and show the optimal error estimates and superconvergence property. We also verify the performance of our numerical schemes by some numerical examples.
AB - The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and linear momentum of the equation have not been considered. In this paper, we propose high-order numerical methods to solve the Klein-Gordon equation, present the energy and linear momentum conservation properties of our numerical schemes, and show the optimal error estimates and superconvergence property. We also verify the performance of our numerical schemes by some numerical examples.
KW - Energy-conserving method
KW - High-order numerical methods
KW - Linear momentum conservation
KW - Local discontinuous Galerkin methods
KW - Optimal error estimates
KW - Superconvergence
KW - The Klein-Gordon equation
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U2 - 10.3390/math6100200
DO - 10.3390/math6100200
M3 - Article
AN - SCOPUS:85054854114
SN - 2227-7390
VL - 6
JO - Mathematics
JF - Mathematics
IS - 10
M1 - 200
ER -