A systematic approach to the construction of hybrid time- and frequency-domain algorithms derived from finite-difference operators is presented. The idea originates from projection formalism in a finite-dimensional vector space. We show that various algorithms can be obtained by an appropriate transformation of finite-difference operators. In the developed formalism, a transformation can be applied to the entire or a part of the computational domain, which can be easily employed to construct hybrid algorithms that combine, for instance, multiresolution techniques with eigenfunction expansion or finite differences. The stability of the developed time-domain hybrid schemes is shown. Numerical examples are given, illustrating different issues related to presented algorithms.
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