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Numerical Solution of Integro-Differential Equations with Local Polynomial Regression

¹ School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China
² School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China
³ School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China
⁴ Library, Chongqing University of Technology, Chongqing, China
⁵ School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China

Open Journal of Statistics·Volume 02 (2012)·Pages 352–355·Published 27 June 2012·DOI10.4236/ojs.2012.23043

Abstract

In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ b a 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∫ x a 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.

KeywordsIntegro-Differential EquationsLocal Polynomial RegressionKernel Functions

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Numerical Solution of Integro-Differential Equations with Local Polynomial Regression

Abstract

References (14)