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New Stable Numerical Inversion of Generalized Abel Integral Equation

  • Shweta Pandey
  • Sandeep Dixit
  • S. R. Verma
Chapter
Part of the Asset Analytics book series (ASAN)

Abstract

A direct technique for the solution of generalized Abel integral equation numerically which is based on Bernstein polynomials multiwavelets-based approximations is presented. The Bernstein polynomials properties and arrangement of Bernstein polynomials multiwavelets are displayed. In our technique, Bernstein multiwavelets-based operational matrices diminish the taken generalized Abel integral equation to algebraic equation system for less demanding calculations. The solidness and precision are checked by comparing the ascertained approximated solution and the known analytical solution, so the proposed strategy is a steady technique for applying to test information with noise. A few numerical cases with figures are solved to indicate convergence and utilization of our strategy.

Keywords

Bernstein polynomials Multiwavelets Abel integral equation 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsHaridwarIndia
  2. 2.Department of MathematicsUniversity of Petroleum and Energy StudiesDehradunIndia

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