The reverse interpolation and its application in the numerical solutions of Fredholm integral equations of the second ki
- PDF / 414,182 Bytes
- 15 Pages / 439.37 x 666.142 pts Page_size
- 34 Downloads / 178 Views
(2019) 38:179
The reverse interpolation and its application in the numerical solutions of Fredholm integral equations of the second kind Seyyed Mahmood Mirzaei1 · Majid Amirfakhrian1 Received: 17 January 2019 / Revised: 8 August 2019 / Accepted: 24 September 2019 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019
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. Keywords Interpolation · Fredholm integral equation · Collocation method Mathematics Subject Classification 97N40 · 45B05 · 41A05
1 Introduction Fredholm integral equations are of practical importance because they are used in various problems such as boundary value problems. Due to the application of integral equations in physics [Flow of heat in a metal bar (Rahman 2007), Thermophoresis and heat generation (Sami and Nasir 2018), Cattaneo–Christov heat flux model (Sami et al. 2019), Brownian movement and thermophoretic aspects (Sami and Shehzad 2019)], mechanical problems [Stokes flow (Ata and Sahin 2018), Bioconvection flow (Waqas et al. 2019), Radiative flow (Waqas et al. 2019)] and engineering [Mutual coupling between dipole antennas (Katagi et al. 2016)], much effort has been made to study the solutions and the theory of integral equations
Communicated by Hui Liang.
B 1
Majid Amirfakhrian [email protected] Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
123
179
Page 2 of 15
S. M. Mirzaei, M. Amirfakhrian
such as LSMR iterative method for solving linear Fredholm integral equations (Asgari et al. 2019), Regularization method for Fredholm integral equations (Benrabia and Guebbai 2018) and (Babolian et al. 2008; Barrera et al. 2018; Laurita 2017; Liu 2009; Long and Nelakanti 2007; Muller and Varnhorn 2011; Wazwaz 2011). Shepard method for constructing a global interpolating function by blending local interpolating functions using local-support weight functions [In order for the overall method to be local, it is necessary that the weight functions have local-support, that is, be nonzero over a bounded region, or
Data Loading...
