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Liao, Hui-qing; Fu, Ying; Ma, He-ping

A space-time spectral method for the 1-D Maxwell equation. (English) Zbl 1484.65262

AIMS Math. 6, No. 7, 7649-7668 (2021).
Summary: A Legendre-tau space-time spectral method is established for the 1-D Maxwell equation. The polynomials of different degrees are used to approximate the electric and magnetic fields, respectively, so that they can be decoupled in computation. Also, the time multi-interval Legendre-tau space-time spectral method is considered to keep the long-time computation stable. Error estimates for the method of single and multi-internal are given, respectively. Moreover, the space-time spectral method is applied to the numerical solutions of the 1-D nonlinear Maxwell equation and describes its implicit-explicit iteration scheme. Numerical examples are compared with some other methods, which verifies the effectiveness of the methods for the 1-D Maxwell equation.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q61 Maxwell equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
78M22 Spectral, collocation and related methods applied to problems in optics and electromagnetic theory

Keywords:

Maxwell equation; space-time spectral method; Legendre polynomial; interval decomposition; error estimate
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References:

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