K. Maleknejad and F. Mizaee, “Numerical Solution of Integro-Differential Equations by Using Rationalized Haar Functions Method,” International Journal of System Mathematics, Vol. 35, No. 10, 2006, pp. 1735-1744. doi 10.1108/03684920610688694

has been cited by the following article:

• 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.