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The reverse interpolation and its application in the numerical solutions of Fredholm integral equations of the second kind

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Abstract

In this paper, we introduce a new interpolation method that is easy to use and its interpolating function can be explicitly expressed. This interpolation method can be used for a wide spectral type of functions, since it has the ability to change the form of the interpolating function. This interpolation inspired by the Shepard type interpolation. We examine the ability of this interpolation to piecewise functions and rational functions and compare it with Lagrange interpolation and linear interpolation by using Bernstein polynomials basis. We applied this interpolation for an integral equation, and we presented a linear system of equations to approximate the solution of a Fredholm integral equation by collocation method. In the collocation method, the Reverse Interpolation expresses the approximate solution in the form of a linear combination of some basic functions. Several examples are presented to illustrate the effectiveness of the proposed method and the numerical results confirm the desired accuracy.

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Authors and Affiliations

  1. Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    Seyyed Mahmood Mirzaei & Majid Amirfakhrian

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  1. Seyyed Mahmood Mirzaei
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  2. Majid Amirfakhrian
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Correspondence to Majid Amirfakhrian.

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Communicated by Hui Liang.

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Mirzaei, S.M., Amirfakhrian, M. The reverse interpolation and its application in the numerical solutions of Fredholm integral equations of the second kind. Comp. Appl. Math. 38, 179 (2019). https://doi.org/10.1007/s40314-019-0950-1

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  • DOI: https://doi.org/10.1007/s40314-019-0950-1

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