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Journal Paper

The Reverse Interpolation and its Application in the Numerical Solutions of Fredholm Integral Equations of the Second Kind

Computational and Applied Mathematics, Vol. 38, Article Number: 179, (2019).

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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Journal Paper

Modified Neumann Series for Solving Fredholm Integral Equations

Applied Mathematical Sciences, Vol. 3 No. 13, (2009), 623-628

In this paper we present a modification to Neumann series method for solving Fredholm integral equations. We create a perturbation in left side of a Fredholm integral equation and we show the decrement of the upper bound for the error.

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conference paper

A Modification of Neumann Series for Solving Fredholm Integral Equations

Regional Mathematics Conference (2008) Rasht, Iran.

In this work a modification of Neumann series used for solving linear Fredholm integral equations.

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@Copyright 2020  Dr. Amirfakhrian  | Powered by Applied Plan