An improved reproducing kernel method for Fredholm integro-differential type two-point boundary value problems. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Xue, Qing; Niu, Jing; Yu, Dandan; Ran, Cuiping
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 5(2018)
• Page Start: 1015
• Page End: 1023
• Publication Date: 2018-05-04
• Subjects: Reproducing kernel method -- Fredholm integro-differential equations -- numerical solution; 30E25 -- 34K28 -- 47B32; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1322201
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this work, an improved reproducing kernel method to find the numerical solution of Fredholm integro-differential equation type boundary value problems has been developed. Based on the good properties of reproducing kernel function and the conjugate operator, the solution representation is obtained. Meanwhile, we prove that the approximation converges to the exact solution uniformly. After that the convergence estimates are derived.