PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2015 | 1 | 1 |
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Słowa kluczowe
Wydawca

Rocznik
Tom
1
Numer
1
Opis fizyczny
Daty
otrzymano
2015-05-25
zaakceptowano
2015-08-03
online
2015-10-19
Twórcy
autor
  • Faculty of Mathematics and
    Computer Science, University of Tartu, Liivi 2, 50409 Tartu, Estonia
autor
  • Faculty of Mathematics and
    Computer Science, University of Tartu, Liivi 2, 50409 Tartu, Estonia
Bibliografia
  • [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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_1515_wwfaa-2015-0001
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.