Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 40, Issue 4, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-021-01508-4
Keywords
Klein-Gordon-Dirac equation; Compact finite difference scheme; Solvability; Conservation; Error analysis
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Funding
- Hebei Natural Science Foundation of China [A2014205136]
- National Natural Science Foundation of China [11571181]
- Natural Science Foundation of Jiangsu Province [BK20171454]
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A conservative fourth-order compact finite difference scheme for the Klein-Gordon-Dirac equation with periodic boundary conditions is proposed and analyzed in this paper. The scheme conserves total mass and energy at the discrete level, with a convergence rate of O(h^4 + τ^2) in l(infinity)-norm. Numerical experiments confirm the theoretical analysis presented.
In this paper, we propose and analyze a conservative fourth-order compact finite difference scheme for the Klein-Gordon-Dirac equation with periodic boundary conditions. Based on matrix knowledge, we convert the point-wise form of the proposed compact scheme into equivalent vector form and analyze its conservative and convergence properties. We prove that the new scheme conserves the total mass and energy in the discrete level and the convergence rate of the scheme, without any restrictions on the grid ratio, is at the order of O(h(4) + tau(2)) in l(infinity)-norm, where h and tau are spatial and temporal steps, respectively. The techniques for error analysis include the energy method and the mathematical induction. The numerical experiments are carried out to confirm our theoretical analysis.
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