Unconditionally stable FDTD method based on Chebyshev polynomials—Chebyshev(CS)FDTD

An unconditionally stable solution using Chebyshev polynomials is proposed for the finite-difference time-domain (FDTD) method. The orthogonality and recurrence of Chebyshev polynomials are used to reconstruct the signal, and Chebyshev polynomials differential matrix is established to realize the transformation of time-domain Maxwell's equations to the Chebyshev domain. The examples show that error is below −50dB when compared with the conventional FDTD method.