## Abstract and Applied Analysis

### Solving a System of Linear Volterra Integral Equations Using the Modified Reproducing Kernel Method

#### Abstract

A numerical technique based on reproducing kernel methods for the exact solution of linear Volterra integral equations system of the second kind is given. The traditional reproducing kernel method requests that operator a satisfied linear operator equation $Au=f$, is bounded and its image space is the reproducing kernel space ${W}_{2}^{1}[a,b]$. It limits its application. Now, we modify the reproducing kernel method such that it can be more widely applicable. The n-term approximation solution obtained by the modified method is of high accuracy. The numerical example compared with other methods shows that the modified method is more efficient.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 196308, 5 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393449741

Digital Object Identifier
doi:10.1155/2013/196308

Mathematical Reviews number (MathSciNet)
MR3132542

Zentralblatt MATH identifier
1291.65391

#### Citation

Yang, Li-Hong; Li, Hong-Ying; Wang, Jing-Ran. Solving a System of Linear Volterra Integral Equations Using the Modified Reproducing Kernel Method. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 196308, 5 pages. doi:10.1155/2013/196308. https://projecteuclid.org/euclid.aaa/1393449741

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