Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Regularization-direct Method to Numerically Solve First Kind Fredholm Integral Equation

  • Masouri, Zahra (Department of Mathematics, Islamshahr Branch, Islamic Azad University (IAU)) ;
  • Hatamzadeh, Saeed (Department of Electrical Engineering, Islamshahr Branch, Islamic Azad University (IAU))
  • Received : 2019.06.07
  • Accepted : 2020.05.30
  • Published : 2020.12.31
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Abstract

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.

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References

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