In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied to analysis of signal of any nature - in computer science, engineering, economics, social studies, decision making etc. The variety of types of signals need a diversity of adequate complementary specific methods, in an addition to common algorithms. As an example, one may refer to vibrations, stability of mechanisms. Many mathematical equations are common in Science, Technics and Humanities.
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