On Nonlinear Urysohn Integral Equation Via Measures of Noncompactness and Numerical Method to Solve It

Document Type : Research Paper

Authors

1 Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran

2 2Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

Abstract

In this study, we present the existence of solutions for Urysohn integral equations. By using the techniques of noncompactness measures, we employ the basic fixed point theorems such as Petryshyn's fixed point theorem to obtain the mentioned aim in Banach algebra. Then this paper presents a numerical approach based on Haar wavelets to solve the equation. This numerical method does not lead to a nonlinear algebraic equations system. Conducting numerical experiments confirm the theoretical results of the applied method and endorse the accuracy of the method.

Keywords

References

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Global Analysis and Discrete Mathematics
Volume 6, Issue 2
November 2021
Pages 309-320

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History

  • Receive Date: 02 April 2021
  • Revise Date: 22 June 2021
  • Accept Date: 23 June 2021

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