A Method for Numerical Solution of Third-Kind Volterra Integral Equations Using Krall-Laguerre Polynomials

Subject Areas : International Journal of Industrial Mathematics

پروانه  جمی ¹ (گروه ریاضی، واحد کرج، دانشگاه آزاد اسلامی، کرج، ایران.)
الهام  هاشمی زاده ² (گروه ریاضی، واحد کرج، دانشگاه آزاد اسلامی، کرج، ایران.)

Received: 2021-04-12 Accepted : 2021-06-26 Published : 2022-01-01

Keywords: Krall-Laguerre ‎Polynomials, ‎Approximation, ‎ Krall-Hahn Orthogonal Polynomials, Third-Kind Integral ‎Equations, Analytical solution‎‎. Fredholm Integral Equations,

Abstract :

The numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper we propose a new method for numerical solution of linear integral equations of third kind. The proposed method is based on the approximation of the unknown function with Krall-Laguerre polynomials. This method has a simple computation with a quite acceptable approximate solution. Moreover, we obtain an estimate of the error bound for suggested method. Two examples are also presented to show the efficiency of the proposed method.

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