RETRACTED CHAPTER: A Collocation Method for Integral Equations in Terms of Generalized Bernstein Polynomials

2016 ◽  
pp. 271-285
Author(s):  
Vinai K. Singh ◽  
A. K. Singh
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Bernstein Polynomials ◽  
Generalized Bernstein Polynomials

scholarly journals A variant of the collocation method for the Fredholm integral equations of the second kind

2017 ◽  
pp. 187-191
Author(s):  
С.А. Соловьева
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Bernstein Polynomials ◽  
Fredholm Integral Equations ◽  
Smooth Functions

Предложен и теоретически обоснован специальный вариант метода коллокации на базе полиномов Бернштейна приближенного решения интегральных уравнений Фредгольма второго рода в пространстве гладких функций. A special variant of the collocation method based on Bernstein polynomials is proposed and theoretically substantiated for the approximate solution of Fredholm integral equations of the second kind in the space of smooth functions.

Collocation method for Fredholm and Volterra integral equations

Kybernetes ◽  
2013 ◽  
Vol 42 (3) ◽  
pp. 400-412 ◽  
Author(s):  
Jalil Rashidinia ◽  
Zahra Mahmoodi
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations

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) 

Generalized Bernstein Polynomials

2004 ◽  
Vol 44 (1) ◽  
pp. 63-78 ◽  
Author(s):  
Stanisław Lewanowicz ◽  
Paweł Woźny
Keyword(s):  
Bernstein Polynomials ◽  
Generalized Bernstein Polynomials
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