Haar Wavelet: History and Its Applications

  • Mahendra Kumar Jena
  • Kshama Sagar SahuEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 308)


In this paper, we have given a brief history of the Haar wavelet. Later the operational matrix which is obtained from Haar wavelet is used to find the numerical solutions of some differential equations. The solutions thus obtained from operational matrix method are compared with exact solution as well as solution from Runge-Kutta method and Modified Euler’s method is presented.


Haar wavelet Operational matrix Initial value problem 

AMS Classification

65L05 65L07 


  1. 1.
    Chen, C., Hsiao, C.H.: Haar wavelet method for solving lumped and distributed parameter system. IEE Proc. Control Theory Appl. 144, 87–94 (1997)CrossRefGoogle Scholar
  2. 2.
    Chui, C.K.: An Introduction to Wavelets. Academic Press, San Diego, CA (1992)zbMATHGoogle Scholar
  3. 3.
    Daubechies, I.: Ten Lectures on Wavelet. SIAM Philadelphia (1992)Google Scholar
  4. 4.
    Davis, M.E.: Numerical Methods and Modeling for Chemical Engineers, pp. 54–63. Dover Publication, New York (2013)Google Scholar
  5. 5.
    Graps, A.: An Introduction to wavelet. IEEE Comput. Sci. Eng. 2, 50–61 (1995)CrossRefGoogle Scholar
  6. 6.
    Jena, M.K., Sahu, K.S.: Haar wavelet operational matrix method to solve initial value problems: a short survey. Int. J. Appl. Comput. Math. 3, 3961–3975 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lepik, U.: Numerical solution of differential equations using Haar wavelets. Math. Comput. Simul. 68, 127–143 (2005)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lepik, U., Hein, H.: Haar Wavelets With Applications. Springer, Berlin (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsVeer Surendra Sai University of TechnologyBurla, SambalpurIndia

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