Publication:
Numerical solution of integral equations by using local polynomial regression

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Date
2008-04
Authors
Çağlar, Nazan
Çağlar, Hikmet
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EUDOXUS PRESS, LLC, 1424 BEAVER TRAIL DRIVE, CORDOVA, TN 38016 USA
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Abstract

In this paper, we find numerical solution of

x(t) + lambda integral(b)(a)k(t,s)x(s)ds = y(t) a <= t <= b

or

x(t) + lambda integral(b)(a) k(t,s)x(s)ds = y(t) a <= t <= b, a <= s <= b

by Local Polynomial Regression (LPR). We shown that, present new method is powerful in solving both Fredholm and Volterra integral equations. The method is tested on some model problems to demonstrate its usefulness. The convergence of the method is discusses.

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Keywords
integral equations , local polynomial regression , Kernel functions , integral denklemler , yerel polinom regresyon , çekirdek fonksiyonları
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