Numerical Solution of Integro-Differential Equations with Local Polynomial Regression

Liyun Su, Tianshun Yan, Yanyong Zhao, Fenglan Li, Ruihua Liu

Library, Chongqing University of Technology, Chongqing, China.
School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China.

DOI: 10.4236/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.

Keywords

Integro-Differential Equations; Local Polynomial Regression; Kernel Functions

Conflicts of Interest

The authors declare no conflicts of interest.

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