10.1007/s40096-020-00342-9

An efficient solution of system of generalized Abel integral equations using Bernstein polynomials wavelet bases

  • Shweta Pandey1,
  • Sandeep Dixit*2,
  • S. R. Verma1,
  1. Department of Mathematics and Statistics, Gurukula Kangri Vishwavidyalaya, Haridwar, 249404, IN
  2. Department of Mathematics, University of Petroleum and Energy Studies, Dehra Dun, 248007, IN

Published in Issue 2020-07-14

How to Cite

Pandey, S., Dixit, S., & Verma, S. R. (2020). An efficient solution of system of generalized Abel integral equations using Bernstein polynomials wavelet bases. Mathematical Sciences, 14(3 (September 2020). https://doi.org/10.1007/s40096-020-00342-9
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Abstract

Abstract This work introduces a direct method based on orthonormal Bernstein polynomials wavelet bases, to present a stable algorithm for numerical inversion of a system of generalized Abel integral equations. The application of all the currently existing numerical inversion methods was strictly limited to only one portion of the generalized Abel integral equations. The proposed method is quite accurate, and several numerical illustrations demonstrate the convergence and utilization of the proposed method compared to some of the preexisting numerical solution techniques. The permanence of the numerical result under the effect of small perturbation in input data has been examined, which is depicted with the use of numerical illustrations.

Keywords

  • Bernstein polynomials,
  • Abel inversion,
  • Wavelet bases,
  • System of generalized Abel integral equations

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