Application of the energy-based stability condition for the spatial wavelet-transformed FDTD scheme
This paper presents an energy-based stability analysis on the classical FDTD scheme using so-called Lyapunov functions. Following a short introduction on a spatial wavelet-transformed FDTD method which has multi-resolution capabilities and notes that only neglecting wavelet coefficients in the specific resolution levels makes the scheme highly productive in comparison to the classical scheme. The fact of negligence makes the scheme inaccessible to classical stability analysis. The energy-based stability analysis is able to derive a condition and we prove their flexibility by application on the spatial wavelet-transformed FDTD scheme with and without neglected coefficients.
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