CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Haar Wavelet Matrices for the Numerical Solutions of Differential Equations

by Sangeeta Arora, Yadwinder Singh Brar, Sheo Kumar
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 97 - Number 18
Year of Publication: 2014
Authors: Sangeeta Arora, Yadwinder Singh Brar, Sheo Kumar
10.5120/17108-7759

Sangeeta Arora, Yadwinder Singh Brar, Sheo Kumar . Haar Wavelet Matrices for the Numerical Solutions of Differential Equations. International Journal of Computer Applications. 97, 18 ( July 2014), 33-36. DOI=10.5120/17108-7759

@article{ 10.5120/17108-7759,
author = { Sangeeta Arora, Yadwinder Singh Brar, Sheo Kumar },
title = { Haar Wavelet Matrices for the Numerical Solutions of Differential Equations },
journal = { International Journal of Computer Applications },
issue_date = { July 2014 },
volume = { 97 },
number = { 18 },
month = { July },
year = { 2014 },
issn = { 0975-8887 },
pages = { 33-36 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume97/number18/17108-7759/ },
doi = { 10.5120/17108-7759 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:24:28.836423+05:30
%A Sangeeta Arora
%A Yadwinder Singh Brar
%A Sheo Kumar
%T Haar Wavelet Matrices for the Numerical Solutions of Differential Equations
%J International Journal of Computer Applications
%@ 0975-8887
%V 97
%N 18
%P 33-36
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Haar Wavelets has become important tool for solving number of problems of science and engineering. In this paper a computational scheme is implemented using Haar matrices to find the numerical solution of differential equations with known initial and boundary conditions. We also presented exact solution, numerical solution and absolute error. Numerical experiments presented here are comparable with the available data. The algorithm used in this is very simple and easy to implement.

References
  1. Stromberg, J. O. , 1981. In Proceedings of Harmonic Analysis, University of Chicago, 475-494.
  2. Grossmann, A. , and Morlet, J. , 1984. SIAM J. Math. Anal. 15, 723.
  3. Meyer, Y. , 1989. Analysis at Urbana 1: Analysis in Function Spaces Cambridge University Press, Cambridge.
  4. Mallat, S. G. , 1989. Trans. Amer. Math. Soc. 315,69.
  5. Daubechies, I. , 1988. "Orthonormal bases of compactly supported wavelets", Comm. Pure Appl. Math. , 909-996.
  6. Strang, G. , 1989. SIAM Rev. 31, 614.
  7. Hsiao, C. H. , 2004. "Haar wavelet approach to linear stiff systems", Mathematics and Computers in Simulation, 561-567.
  8. Daubechies, I. , 1992. Ten Lectures on Wavelets (SIAM, Philadelphia,)
  9. Chui, C. K. , 1992. "An introduction to wavelets" (Academic Press, Boston, MA).
  10. Lepik, ULO. , 2005. Numerical solution of differential equations using Haar wavelets, Mathematics and Computers in Simulation, 127-143.
  11. Daubechies, I. , 1992. "Ten Lectures on Wavelets, SIAM, Philadelphia, PA".
  12. Kaiser, G. , 1994. "A friendly guide to wavelets," Boston: Birkhauser.
  13. Lepik, U. , 2007. "Numerical Solution of Evolution Equations" by the Haar Wavelet Method. Appl. Math. and Comput. , 185, 695-704.
  14. Chen, C. F. , and Hsiao, C. H. , 1997. "Haar Wavelet Method for Solving Lumped and Distributed Parameter Systems," IEE Proc, Number 144 in Control Theory Appl. , 87-94.
  15. Hsiao, C. H. , 1997. "State Analysis of Linear Time Delayed Systems via Haar Wavelets," Math. Comp. Simulat. , 44: 457-470.
  16. Cattani, C. , 2004. "Haar Wavelets Based Technique in Evolution Problems," Proc. Estonian Acad. Set Phys. Math. , 1: 45-63.
  17. Siddiqui, Abul Hasan. , 2003. "Wavelet Method for Partial Differential Equations and Image Processing, Numerical Methods," Wavelet Methods and Image Processing ISBN: 978-0-8247-4097-9, ISBN: 978-0-203-91301-7, doi: 10. 1201/97802039 13017. Ch 11.
  18. Hariharan, G. , 2013. "An Overview of Haar Wavelet Method for Solving Differential and Integral Equations," World Applied Sciences Journal, 23, 01-14
  19. Haar, A. , 1910. "Zur Theorie Der Orthogonalen Funktionsysteme," Math. Ann. 69, 331-371.
  20. Hsiao, C. H. and S. P. Wu, 2007 "Numerical Solution of Time-Varying Functional Differential Equations" via Haar Wavelets. Appl. Math. Comput. , 188 (1): 1049-1058.
Index Terms

Computer Science
Information Sciences

Keywords

Haar wavelets Haar functions Operational matrix Differential equation.

Powered by PhDFocusTM