TITLE:
Numerical Solution of Integro-Differential Equations with Local Polynomial Regression
AUTHORS:
Liyun Su, Tianshun Yan, Yanyong Zhao, Fenglan Li, Ruihua Liu
KEYWORDS:
Integro-Differential Equations; Local Polynomial Regression; Kernel Functions
JOURNAL NAME:
Open Journal of Statistics,
Vol.2 No.3,
July
6,
2012
ABSTRACT: In this paper, we try to find numerical solution of
y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b
or
y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b
by using Local polynomial regression (LPR) method. The numerical solution shows that this method is powerful in solving integro-differential equations. The method will be tested on three model problems in order to demonstrate its usefulness and accuracy.