On spline approximation for a class of integral equations. I: Galerkin and collocation methods with piecewise polynomials

1988 ◽  
Vol 10 (5) ◽  
pp. 543-559 ◽  
Author(s):  
Johannes Elschner
Keyword(s):  
Integral Equations ◽  
Spline Approximation ◽  
Collocation Methods ◽  
Piecewise Polynomials ◽  
Galerkin And Collocation Methods

On Projective Methods of Approximate Solution of Singular Integral Equations

1996 ◽  
Vol 3 (5) ◽  
pp. 457-474
Author(s):  
A. Jishkariani ◽  
G. Khvedelidze
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Collocation Methods ◽  
Projective Methods ◽  
Galerkin And Collocation Methods

Abstract The estimate for the rate of convergence of approximate projective methods with one iteration is established for one class of singular integral equations. The Bubnov–Galerkin and collocation methods are investigated.

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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