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Approximations of a function whose first and second derivatives belonging to generalized Hölder’s class by extended Legendre wavelet method and its applications in solutions of differential equations

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Abstract

In this paper, the generalized Hölder’s class and extended Legendre wavelet are studied. The wavelet approximations of a function whose first and second derivatives belonging to generalized Hölder’s class by extended Legendre wavelets have been determined. Two corollaries have been obtained by the main theorems of this paper. Linear and non-linear differential equations have been solved by extended Legendre wavelet methods.

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References

  1. DeVore, R.A.: Nonlinear Approximation, Acta Numerica, vol. 7, pp. 51–150. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  2. Morlet, J., Arens, G., Fourgeau, E., Giard, D.: Wave propagation and sampling theory, part I; complex signal and scattering in multilayer media. Geophysics 47(2), 203–221 (1982)

    Article  Google Scholar 

  3. Morlet, J., Arens, G., Fourgeau, E., Giard, D.: Wave propagation and sampling theory, part II; sampling theory and complex waves. Geophysics 47(2), 222–236 (1982)

    Article  Google Scholar 

  4. Meyer, Y.: Wavelets; their past and their future. In: Meyer, Y., Roques, S. (eds.) Progress in Wavelet Analysis and (Applications) (Toulouse, 1992), pp. 9–18. Frontieres, Gif-sur-Yvette (1993)

  5. Debnath, L.: Wavelet Transform and Their Applications. Birkhauser Boston, Massachusetts (2002)

    Book  Google Scholar 

  6. Shyam Lal and Vivek Kumar Sharma: On wavelet approximation of a function by Legendre wavelet methods. Funct. Anal. Approx. Comput. 9(2), 11–19 (2017)

    MathSciNet  MATH  Google Scholar 

  7. Mohammadi, F., Hosseini, M.M., Mohyud-Din, S.T.: An extended Legendre wavelet method for solving differential equations with non-analytic solutions. J. Math. Ext. 8(4), 55–74 (2014)

    MathSciNet  Google Scholar 

  8. Nanshan, L., Lin, E.B.: Legendre wavelet method for numerical solutions of partial differential equations. Numer. Methods Partial Diff. Eq. 26, 81–94 (2009)

    MathSciNet  MATH  Google Scholar 

  9. Das, G., Ghosh, Tulika, Ray, B.K.: Degree of approximation of functions by their Fourier series in the generalized Hölder metric. Proc. Indian Acad. Sci. (Math. Sci.) 106(2), 139–153 (1996)

    Article  MathSciNet  Google Scholar 

  10. Zygmund, A.: Trigonometric Series, vol. I. Cambridge University Press, Cambridge (1959)

    MATH  Google Scholar 

Download references

Acknowledgements

Shyam Lal, one of the authors, is thankful to DST - CIMS for the encouragement to this work. Sharma Priya R, one of the authors, is grateful to C.S.I.R. (Council of Scientific and Industrial Research), India for providing financial assistance in the form of JRF (Junior Research Fellowship vide letter No. 17/12/2017 (ii) EU-V (Dated 17/11/2018) for this research work.

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  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Shyam Lal & Sharma Priya R.

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  1. Shyam Lal
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  2. Sharma Priya R.
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Correspondence to Shyam Lal.

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Lal, S., Sharma, P.R. Approximations of a function whose first and second derivatives belonging to generalized Hölder’s class by extended Legendre wavelet method and its applications in solutions of differential equations. Rend. Circ. Mat. Palermo, II. Ser 70, 959–993 (2021). https://doi.org/10.1007/s12215-020-00526-1

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  • DOI: https://doi.org/10.1007/s12215-020-00526-1

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