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J. Pour-Mahmoud, M. Y. Rahimi-Ardabili and S. Shahmorad, “Numerical Solution of the System of Fredholm Integro-Differential Equations by the Tau Method,” Applied Mathematics Computation, Vol. 168, No. 1, 2005, pp. 465-478. doi:10.1016/j.amc.2004.09.026

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.