Abstract: Taking the 1-D nonlinear Maxwell 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 equations, multidomain Legendre tau method, stability, convergence