## Abstract and Applied Analysis

### Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations

#### Abstract

This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution $u(x)$ is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ${u}_{n}(x)$ is obtained and it is proved to converge to the exact solution $u(x)$. Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 839836, 16 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.aaa/1355495858

Digital Object Identifier
doi:10.1155/2012/839836

Mathematical Reviews number (MathSciNet)
MR2969993

Zentralblatt MATH identifier
1253.65200

#### Citation

Abu Arqub, Omar; Al-Smadi, Mohammed; Momani, Shaher. Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations. Abstr. Appl. Anal. 2012 (2012), Article ID 839836, 16 pages. doi:10.1155/2012/839836. https://projecteuclid.org/euclid.aaa/1355495858

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