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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

up.

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Dates

online

19 - 10 - 2015

received

25 - 5 - 2015

accepted

3 - 8 - 2015

References

- [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]

Document Type

Publication order reference

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YADDA identifier

bwmeta1.element.-psjd-doi-10_1515_wwfaa-2015-0001