A new reproducing kernel method with higher convergence order for solving a Volterra–Fredholm integral equation. (April 2020)

• Record Type: Journal Article
• Authors: Du, Hong; Chen, Zhong
• Is Part Of: Applied mathematics letters. Volume 102(2020)
• Publication Date: 2020-04
• Subjects: Reproducing kernel -- Convergence order -- Oscillation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106117
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In the paper, linear Volterra–Fredholm integral equations of the second kind are considered in a reproducing kernel space. The approximate solution is gotten by constructing a uniquely solvable system of linear algebraic equations. Our important contributions are to provide convergence order theorems of the scheme using spline function theories and propose a new scheme with high convergence order for solving the approximate solutions to oscillation and non-oscillation of exact solutions.