一维非线性Maxwell方程的多区域Legendre tau方法

doi:10.12066/j.issn.1007-2861.2278

Abstract

Abstract: 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.

Key words: nonlinear Maxwell’s equation, multidomain Legendre tau method, stability, convergence

CLC Number:

O241.82

YAO Jiaqian, MA Heping. A multidomain Legendre tau method for 1-D nonlinear Maxwell’s equations[J]. Journal of Shanghai University（Natural Science Edition）, 2025, 31(6): 1087-1102.

References

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A multidomain Legendre tau method for 1-D nonlinear Maxwell’s equations

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