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2015 | 1 | 1 |
Article title

Application of the Haar wavelet method for
solution the problems of mathematical calculus

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In recent times the wavelet methods have obtained
a great popularity for solving differential and integral
equations. From different wavelet families we consider
here the Haar wavelets. Since the Haar wavelets are
mathematically most simple to be compared with other
wavelets, then interest to them is rapidly increasing and
there is a great number of papers,where thesewavelets are
used tor solving problems of calculus. An overview of such
works can be found in the survey paper by Hariharan and
Kannan [1] and also in the text-book by Lepik and Hein [2].
The aim of the present paper is more narrow: we want to
popularize our method of solution, which is published in
19 papers and presented in the text-book [2]. This method
is quite universal, since a large group of problems can be
solved by a unit approach. The paper is organised as follows. In Section 1 fundamentals
of the wavelet method are described. In Section 2
the Haar wavelet method and solution algorithms are presented.
In Sections 3-9 different problems of calculus and
structural mechanics are solved. In Section 10 the advantageous
features of the Haar wavelet method are summed
Physical description
19 - 10 - 2015
25 - 5 - 2015
3 - 8 - 2015
  • [1] Hariharan G., Kannan K., An overview of Haar wavelet methodfor solving differential and integral equations. World AppliedSciences Journal, 25, (2013 ) 1 – 14.
  • [2] Lepik Ü, Hein H., HaarWaveletswith Applications, Springer, 207pp., 2014.
  • [3] Daubechies I., Orthonormal bases of compactly supportedwavelets, Commun. Pure Appl. Math., 41, (1988) 909 – 996.[Crossref]
  • [4] Chen C., Hsiao C., Haar wavelet method for solving lumped anddistributed-parameter systems, IEEE, Proc. Control Theory Appl.144, (1997) 87-94.
  • [5] Basdevant C., Devillle M., Haldenwang P., Lacroix J., QuazzaniJ., Peyret R., Orlandi P., Patera A., Spectral and finite differencesolutions of the Burgers equation, Comput. Fluids, 14, (1986)23-41.[Crossref]
  • [6] Timoshenko S., Theory of Elastic Stability, McGraw-Hill BookCompany, New-York, 1936.
  • [7] Orhan S., Anaysis of free and forced vibration of a cracked cantileverbeam, NDT&E Int. 40, 443-450, 2007.[WoS]
  • [8] Filipich C.P., Cortinez M.B.R.H., Natural Frequencies of a TimoshenkoBeam: Exact values by means of a generalized solution,Mecanica Computadonal, 14, (1994) 134-143.
  • [9] Shahba A., Attarnejad R., Marvi M.T., Hajilar S., Free vibrationand stability analysis of axially functionally graded tapered Timoshenkobeams with classical and non-classical boundary conditions,Composites: Part B, 42, (2011) 801-808.[WoS][Crossref]
  • [10] Majak J., Shvartsman B., Karjust K., Mikola M.,Haavajõe A.,Pohlak M, On the accuracy of the Haar wavelet discretizationmethod, Composites: Part B, 80, (2015) 321-327.[Crossref][WoS]
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