scholarly journals Comparative experiment on the numerical solutions of Hammerstein integral equation arising from chemical phenomenon

2016 ◽  
Vol 291 ◽  
pp. 402-409 ◽  
Author(s):  
P.K. Sahu ◽  
S. Saha Ray
Keyword(s):  
Integral Equation ◽  
Numerical Solutions ◽  
Comparative Experiment ◽  
Hammerstein Integral Equation

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) 

On the numerical solutions of Fredholm–Volterra integral equation

2003 ◽  
Vol 146 (2-3) ◽  
pp. 713-728 ◽  
Author(s):  
M.A. Abdou ◽  
Khamis I. Mohamed ◽  
A.S. Ismail
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Numerical Solutions

scholarly journals On a measure of noncompactness in the space of regulated functions and its applications

2018 ◽  
Vol 8 (1) ◽  
pp. 1099-1110 ◽  
Author(s):  
Józef Banaś ◽  
Tomasz Zając
Keyword(s):  
Integral Equation ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Closed Interval ◽  
Hammerstein Integral Equation ◽  
Regular Measure ◽  
Relative Compactness ◽  
Regulated Functions

Abstract In this paper we formulate a criterion for relative compactness in the space of functions regulated on a bounded and closed interval. We prove that the mentioned criterion is equivalent to a known criterion obtained earlier by D. Fraňkova, but it turns out to be very convenient in applications. Among others, it creates the basis to construct a regular measure of noncompactness in the space of regulated functions. We show the applicability of the constructed measure of noncompactness in proving the existence of solutions of a quadratic Hammerstein integral equation in the space of regulated functions.

scholarly journals Stern waves with vorticity

2002 ◽  
Vol 43 (3) ◽  
pp. 321-332 ◽  
Author(s):  
Y. Kang ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Integral Equation ◽  
Numerical Solutions ◽  
Free Surface Flow ◽  
Integral Equation Method ◽  
Surface Flow ◽  
Boundary Integral ◽  
Analytical Relation ◽  
Far Field ◽  
Two Dimensional ◽  
The Waves

AbstractSteady two-dimensional free surface flow past a semi-infinite flat plate is considered. The vorticity in the flow is assumed to be constant. For large values of the Froude number F, an analytical relation between F, the vorticity parameter ω and the steepness s of the waves in the far field is derived. In addition numerical solutions are calculated by a boundary integral equation method.

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