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Computing eigenelements of Sturm-Liouville problems by using Daubechies wavelets

Author

Listed:
  • M. M. Panja

    (Visva-Bharati)

  • M. K. Saha

    (Visva-Bharati)

  • U. Basu

    (University of Calcutta)

  • D. Datta

    (HPD, BARC)

  • B. N. Mandal

    (Indian Statistical Institute)

Abstract

This work is our first step to get multiresolution approximation of eigenelements of Sturm-Liouville problems within bounded domain of varied nature. The formula for obtaining elements of representation of Sturm-Liouville operator involving polynomial coefficients in wavelet basis of Daubechies family have been derived in a form which can be readily used for their computations by a simple computer program. Estimates of errors for both the eigenvalues and eigenfunctions are also presented here. The proposed wavelet-Galerkin scheme based on scale functions and wavelets of Daubechies family having three or four vanishing moments of their wavelets has been applied to get approximate eigenelements of regular and singular Sturm-Liouville problems within bounded domain and compared with the exact or approximate results whenever available. From our study it appears that the proposed method is efficient and rapidly convergent in comparison to other approximation schemes based on variational method in Haar basis or finite difference methods studied by Bujurke et al. [39].

Suggested Citation

  • M. M. Panja & M. K. Saha & U. Basu & D. Datta & B. N. Mandal, 2016. "Computing eigenelements of Sturm-Liouville problems by using Daubechies wavelets," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(3), pages 553-579, September.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:3:d:10.1007_s13226-016-0203-6
    DOI: 10.1007/s13226-016-0203-6
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    Cited by:

    1. Avipsita Chatterjee & M. M. Panja & U. Basu & D. Datta & B. N. Mandal, 2021. "Solving one-dimensional advection diffusion transport equation by using CDV wavelet basis," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(3), pages 872-896, September.

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