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Chebyshev spectral solution of nonlinear Volterra-Hammerstein integral equations

โœ Scribed by Gamal N. Elnagar; M. Kazemi

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
511 KB
Volume
76
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

In this paper, the Chebyshev spectral (CS) method for the approximate solution of nonlinear Volterra-Hammerstein integral equations

is investigated. The method is applied to approximate the solution not to the equation in its original form, but rather to an equivalent equation z(t)= 9(t, y(t)), t E [-1, 1 ]. The function z is approximated by the Nth degree interpolating polynomial z N, with coefficients determined by discretizing 9(t,y(t)) at the Chebyshev-Gauss Lobatto nodes. We then define the approximation to y to be of the form

1 and establish that, under suitable conditions, limu~ yU(t) = y(t) uniformly in t. Finally, a numerical experiment for a nonlinear Volterra-Hammerstein integral equation is presented, which confirms the convergence, demonstrates the applicability and the accuracy of the Chebyshev spectral (CS) method,

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