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Time‐splitting methods with charge conservation for the nonlinear Dirac equation
Author(s) -
Li ShuCun,
Li XiangGui,
Shi FangYuan
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22154
Subject(s) - charge conservation , dirac (video compression format) , mathematics , nonlinear system , dirac equation , computation , partial differential equation , charge (physics) , conservation law , block (permutation group theory) , work (physics) , numerical analysis , mathematical analysis , physics , mathematical physics , algorithm , quantum mechanics , geometry , neutrino
In this work, four numerical time‐splitting methods are proposed for the (1 + 1)‐dimensional nonlinear Dirac equation. All of these methods (or schemes) are proved to satisfy the charge conservation in the discrete level. To enhance the computation efficiency, the block Thomas algorithm is adopted. Numerical experiments are given to test the accuracy order for these schemes, to simulate numerically the binary collision including two standing waves and two moving solitons, meanwhile, the dynamic properties for the nonlinear Dirac equation are discussed. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1582–1602, 2017