Skip to main content
SpringerLink
Log in

Iterative Scheme of Integral and Integro-differential Equations Using Daubechies Wavelets New Transform Method

  • Original Paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

Daubechies wavelet new transform technique is presented for the iterative scheme of linear and nonlinear integral (particularly in Fredholm, Volterra, mixed Volterra–Fredholm integral and integro-differential) equations. Wavelet new prolongation and new restriction operators are established via Daubechies D2 wavelet new filter coefficients. Some of the appearance of the numerical examples that the proposed scheme compromises an efficient and better accuracy with faster convergence in less computation cost, which is justified through the error analysis and computational time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Wazwaz, A.M.: Linear and Nonlinear Integral Equations Methods and Applications. Higher Education Press, Beijing (2011)

    Book  Google Scholar 

  2. Jerri, A.J.: Introduction to Integral Equations with Applications. Wiley, New York (1999)

    MATH  Google Scholar 

  3. Atkinson, K.E.: The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  4. Brandt, A.: Multi-level adaptive solutions to boundary-value problems. Math. Comput. 31, 333–390 (1977)

    Article  MathSciNet  Google Scholar 

  5. Wesseling, P.: An Introduction to Multigrid Methods. Wiley, New York (1992)

    MATH  Google Scholar 

  6. Briggs, W.L., Henson, V.E., McCormick, S.F.: A Multigrid Tutorial. Society for Industrial and Applied Mathematics, Philadelphia (2000)

    Book  Google Scholar 

  7. Trottenberg, U., Oosterlee, C., Schuller, A.: Multigrid. Academic Press, London (2001)

    MATH  Google Scholar 

  8. Hackbusch, W.: Multi-grid Methods and Applications. Springer, Berlin (1985)

    Book  Google Scholar 

  9. Schippers, H.: Application of multigrid methods for integral equations to two problems from fluid dynamics. J. Comput. Phys. 48, 441–461 (1982)

    Article  Google Scholar 

  10. Gáspár, C.: A fast multigrid solution of boundary integral equations. Environ. Softw. 5(1), 26–28 (1990)

    Article  Google Scholar 

  11. Lee, H.: Multigrid method for nonlinear integral equations. Korean J. Comput. Appl. Math. 4, 427–440 (1997)

    Article  MathSciNet  Google Scholar 

  12. Hackbusch, W., Trottenberg, U.: Multigrid Methods. Springer, Berlin (1982)

    Book  Google Scholar 

  13. Wesseling, P.: An Introduction to Multigrid Methods. Wiley, Chichester (1992)

    MATH  Google Scholar 

  14. Chui, C.K.: Wavelets: A Mathematical Tool for Signal Analysis. Society for Industrial and Applied Mathematics, Philadelphia (1997)

    Book  Google Scholar 

  15. Beylkin, G., Coifman, R., Rokhlin, V.: Fast wavelet transforms and numerical algorithms I. Commun. Pure Appl. Math. 44, 141–183 (1991)

    Article  MathSciNet  Google Scholar 

  16. Lepik, Ü., Tamme, E.: Application of the Haar wavelets for solution of linear integral equations. In: Antalya, Turkey—Dynamical Systems and Applications, Proceedings, pp. 395–407 (2005)

  17. Aziz, I., Islam, S.: New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets. J. Comput. Appl. Math. 239, 333–345 (2013)

    Article  MathSciNet  Google Scholar 

  18. Leon, D.D.: A new wavelet multigrid method. J. Comput. Appl. Math. 220, 674–685 (2008)

    Article  MathSciNet  Google Scholar 

  19. Bujurke, N.M., Salimath, C.S., Kudenatti, R.B., Shiralashetti, S.C.: A fast wavelet-multigrid method to solve elliptic partial differential equations. Appl. Math. Comput. 185(1), 667–680 (2007)

    Article  MathSciNet  Google Scholar 

  20. Bujurke, N.M., Salimath, C.S., Kudenatti, R.B., Shiralashetti, S.C.: Wavelet-multigrid analysis of squeeze film characteristics of poroelastic bearings. J. Comput. Appl. Math. 203, 237–248 (2007)

    Article  MathSciNet  Google Scholar 

  21. Bujurke, N.M., Salimath, C.S., Kudenatti, R.B., Shiralashetti, S.C.: Analysis of modified Reynolds equation using wavelet-multigrid scheme. Int. J. Numer. Methods Partial Differ. Equ. 23, 692–705 (2007)

    Article  MathSciNet  Google Scholar 

  22. Avudainayagam, A., Vani, C.: Wavelet based multigrid methods for linear and nonlinear elliptic partial differential equations. Appl. Math. Comput. 148, 307–320 (2004)

    Article  MathSciNet  Google Scholar 

  23. Wang, G., Dutton, R.W., Hou, J.: A fast wavelet multigrid algorithm for solution of electromagnetic integral equations. Microw. Opt. Technol. Lett. 24(2), 86–91 (2000)

    Article  Google Scholar 

  24. Shiralashetti, S.C., Kantli, M.H., Deshi, A.B., Mutalik Desai, P.B.: A modified wavelet multigrid method for the numerical solution of boundary value problems. J. Inf. Opt. Sci. 38(1), 151–172 (2017)

    MathSciNet  Google Scholar 

  25. Shiralashetti, S.C., Kantli, M.H., Deshi, A.B.: New wavelet based full-approximation scheme for the numerical solution of nonlinear elliptic partial differential equations. Alex. Eng. J. 55(3), 2797–2804 (2016)

    Article  Google Scholar 

  26. Lilliam, A.D., Maria, T.M., Victoria, V.: Daubechies wavelet beam and plate finite elements. Finite Elem. Anal. Des. 45, 200–9 (2009)

    Article  MathSciNet  Google Scholar 

  27. Daubechies, I.: Orthonormal bases of compactly supported wavelets. Commun. Pure. Appl. Math. 41, 909–996 (1988)

    Article  MathSciNet  Google Scholar 

  28. Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelphia (1992)

    Book  Google Scholar 

  29. Kotsireas, I.S.: A Survey on Solution Methods for Integral Equations. The Ontario Research Centre for Computer Algebra, 47 (2008)

  30. Reihani, M.H., Abadi, Z.: Rationalized Haar functions method for solving Fredholm and Volterra integral equations. J. Comput. Appl. Math. 200, 12–20 (2007)

    Article  MathSciNet  Google Scholar 

  31. Babolian, E., Javadi, Sh, Sadeghi, H.: Restarted Adomian method for integral equations. Appl. Math. Comput. 153, 353–359 (2004)

    Article  MathSciNet  Google Scholar 

  32. Rashidinia, J., Parsa, A.: Analytical-numerical solution for nonlinear integral equations of Hammerstein type. Int. J. Math. Model. Comput. 2(01), 61–69 (2012)

    Google Scholar 

  33. Mirzaee, F., Hadadiyan, E.: A collocation method to the solution of Nonlinearfredholm-Hammerstein integral and integro-differential equations. J. Hyper. 2(1), 72–86 (2013)

    MATH  Google Scholar 

  34. Shahsavaran, A.: Numerical Solution of Nonlinear Fredholm-Volterra Integtral Equations via piecewise constant function by collocation method. Am. J. Comput. Math. 1, 134–138 (2011)

    Article  Google Scholar 

  35. Sepehrian, B., Razzaghi, M.: Solution of nonlinear Volterra–Hammerstein integral equations via single-term Walsh series method. Math. Prob. Eng. 5, 547–554 (2005)

    Article  MathSciNet  Google Scholar 

  36. El-Sayed, S.M., Abdel-Aziz, M.R.: A comparison of Adomian’s decomposition method and wavelet-Galerkin method for solving integro-differential equations. Appl. Math. Comput. 136, 151–159 (2003)

    Article  MathSciNet  Google Scholar 

  37. Griebel, M., Knapek, S.: A multigrid homogenization method. Model. Comput. Environ. Sci. 59, 187–202 (1995)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, M.E.S College of Arts, Commerce and Science, Malleswaram, Bengaluru, India

    R. A. Mundewadi

  2. Department of Mathematics, Government First Grade College for Women’s, Bagalkot, India

    B. A. Mundewadi

  3. Department of Mathematics, Biluru Gurubasava Mahaswamiji Institute of Technology, Mudhol, India

    M. H. Kantli

Authors
  1. R. A. Mundewadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. A. Mundewadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. H. Kantli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. A. Mundewadi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mundewadi, R.A., Mundewadi, B.A. & Kantli, M.H. Iterative Scheme of Integral and Integro-differential Equations Using Daubechies Wavelets New Transform Method. Int. J. Appl. Comput. Math 6, 135 (2020). https://doi.org/10.1007/s40819-020-00879-2

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s40819-020-00879-2

Keywords

Mathematics Subject Classification

Search

Navigation