Numerical Solution of Integro-Differential Equations with Local Polynomial Regression

• 作者: Fenglan Li Liyun Su Ruihua Liu Tianshun Yan Yanyong Zhao
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: Integro-Differential EQUATIONS Local POLYNOMIAL Regression KERNEL FUNCTIONS
• 年，卷（期）: 2012,（3）
• 页码范围: 352-355
• 页数: 4页
• 分类号: O1

摘要

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.