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

• Authors: Ü. Lepik , H. Hein
• Languages of publication: EN

Abstracts

EN

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
up.

Keywords

EN

Haar wavelets; applications

• Publisher: De Gruyter Open
• Journal: Waves, Wavelets and Fractals
• Year: 2015
• Volume: 1
• Issue: 1

Dates

online

19 - 10 - 2015

received

25 - 5 - 2015

accepted

3 - 8 - 2015

Contributors

author

Ü. Lepik

• Faculty of Mathematics and
  Computer Science, University of Tartu, Liivi 2, 50409 Tartu, Estonia

author

H. Hein

• Faculty of Mathematics and
  Computer Science, University of Tartu, Liivi 2, 50409 Tartu, Estonia

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]

Identifiers

DOI

10.1515/wwfaa-2015-0001