Numerical solution of time-varying systems by CAS Wavelets
نویسنده
چکیده
Wavelets theory is a relatively new and an emerging area in mathematical research. It has been applied to a wide range of engineering disciplines; particularly, wavelets are very successfully used in signal analysis for wave form representation and segmentations, time frequency analysis and fast algorithms for easy implementation. wavelets permit the accurate representation of a variety of functions and operators. Moreover,wavelets establish a connection with fast numerical algorithms.Therefore, wavelets have been used to approximate the solution of integral equation[1-2].The main advantage of using o wavelets basis is that it reduces the problem into solving a system of algebraic equations. Overall, there are so many different families of wavelets functions which can be used in this method that it is sometimes difficult to select the most suitable one. Beginning from 1991, wavelet technique has been applied to solve integral equations [3-6,12]. Wavelets, as very well-localized functions, are considerably useful for solving integral equations and provide accurate solutions. Also, the wavelet technique allows the creation of very fast algorithms when compared with the algorithms ordinarily used. In this paper, the solution of time-varying systems is obtained by using CAS wavelets. The method is based upon expanding various time functions in the system as their truncated CSA wavelets. The operational matrix is introduced. The operational matrices of integration are utilized to reduce the solution of time varying systems to the solution of algebraic equations.
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