scholarly journals New integral forms of generalized Mathieu series and related applications

2013 ◽  
Vol 7 (1) ◽  
pp. 180-192 ◽  
Author(s):  
Gradimir Milovanovic ◽  
Tibor Pogány
Keyword(s):  
Integral Equation ◽  
Systematic Study ◽  
Fredholm Integral Equation ◽  
Special Functions ◽  
Integral Form ◽  
Integral Representations ◽  
Integration Path ◽  
Integral Expression ◽  
Integral Forms ◽  
Mathieu Series

The main object of this article is to present a systematic study of integral representations for generalized Mathieu series and its alternating variant, and to derive a new integral expression for these special functions by contour integration using rectangular integration path. Also, by virtue of newly established integral form of generalized Mathieu series, we obtain a new integral expression for the Bessel function of the first kind of half integer order, solving a related Fredholm integral equation of the first kind with nondegenerate kernel.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials

2010 ◽  
Vol 2 (2) ◽  
pp. 264-272 ◽  
Author(s):  
A. Shirin ◽  
M. S. Islam
Keyword(s):  
Integral Equation ◽  
Galerkin Method ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Fredholm Integral Equations ◽  
Matrix Formulation ◽  
Piecewise Polynomials ◽  
The Galerkin Method

In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are used as the approximation of basis functions. Examples are considered to verify the effectiveness of the proposed derivations, and the numerical solutions guarantee the desired accuracy.  Keywords: Fredholm integral equation; Galerkin method; Bernstein polynomials. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.4483               J. Sci. Res. 2 (2), 264-272 (2010) 

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