Taking the 1-D nonlinear Maxwell's equation as a model, the multidomain Legendre tau method is studied for the cases of weak discontinuity and discontinuity at the interface of nonhomogeneous media. The leapfrog-Crank-Nicolson scheme is used for time discretization, which is a three-level explicit-implicit method of good stability and easy implementation. The stability of the scheme is proved, and the L2-error estimate of optimal order is obtained. Numerical examples show the effectiveness of the proposed multidomain Legendre tau method for such nonlinear discontinuous problems.
YAO Jiaqian
,
MA Heping
. A multidomain Legendre tau method for 1-D nonlinear Maxwell’s equations[J]. Journal of Shanghai University, 2025
, 31(6)
: 1087
-1102
.
DOI: 10.12066/j.issn.1007-2861.2278
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