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`Abstract and Applied AnalysisVolume 2013 (2013), Article ID 196308, 5 pageshttp://dx.doi.org/10.1155/2013/196308`
Research Article

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

College of Science, Harbin Engineering University, Heilongjiang 150001, China

Received 16 May 2013; Accepted 30 September 2013

Copyright © 2013 Li-Hong Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Y. Ren, B. Zhang, and H. Qiao, “A simple Taylor-series expansion method for a class of second kind integral equations,” Journal of Computational and Applied Mathematics, vol. 110, no. 1, pp. 15–24, 1999.
2. K. Maleknejad and Y. Mahmoudi, “Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block-pulse functions,” Applied Mathematics and Computation, vol. 149, no. 3, pp. 799–806, 2004.
3. S. Yalçınbaş and M. Sezer, “The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials,” Applied Mathematics and Computation, vol. 112, no. 2-3, pp. 291–308, 2000.
4. S. Yalçinbaş, “Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations,” Applied Mathematics and Computation, vol. 127, no. 2-3, pp. 195–206, 2002.
5. E. Deeba, S. A. Khuri, and S. Xie, “An algorithm for solving a nonlinear integro-differential equation,” Applied Mathematics and Computation, vol. 115, no. 2-3, pp. 123–131, 2000.
6. A. Tahmasbi and O. S. Fard, “Numerical solution of linear Volterra integral equations system of the second kind,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 547–552, 2008.
7. E. Babolian, J. Biazar, and A. R. Vahidi, “On the decomposition method for system of linear equations and system of linear Volterra integral equations,” Applied Mathematics and Computation, vol. 147, no. 1, pp. 19–27, 2004.
8. J. Biazar and H. Ghazvini, “He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind,” Chaos, Solitons & Fractals, vol. 39, no. 2, pp. 770–777, 2009.
9. E. Yusufoğlu (Agadjanov), “A homotopy perturbation algorithm to solve a system of Fredholm-Volterra type integral equations,” Mathematical and Computer Modelling, vol. 47, no. 11-12, pp. 1099–1107, 2008.
10. R. Katani and S. Shahmorad, “Block by block method for the systems of nonlinear Volterra integral equations,” Applied Mathematical Modelling, vol. 34, no. 2, pp. 400–406, 2010.
11. M. Rabbani, K. Maleknejad, and N. Aghazadeh, “Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 1143–1146, 2007.
12. M. G. Cui and Z. X. Deng, “On the best operator of interpolation in ${W}_{2}^{1}\left[a,b\right]$,” Mathematica Numerica Sinica, vol. 2, pp. 209–216, 1986.
13. M. Cui and F. Geng, “A computational method for solving one-dimensional variable-coefficient Burgers equation,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1389–1401, 2007.
14. M. Cui and F. Geng, “A computational method for solving third-order singularly perturbed boundary-value problems,” Applied Mathematics and Computation, vol. 198, no. 2, pp. 896–903, 2008.
15. M. Cui and Z. Chen, “The exact solution of nonlinear age-structured population model,” Nonlinear Analysis. Real World Applications, vol. 8, no. 4, pp. 1096–1112, 2007.
16. F. Z. Geng and M. G. Cui, “Solving singular nonlinear two-point boundary value problems in the reproducing kernel space,” Journal of the Korean Mathematical Society, vol. 45, no. 3, pp. 631–644, 2008.
17. M. G. Cui and Y. B. Yan, “The representation of the solution of a kind operator equation $Au=f$,” Journal of Chinese Universities, vol. 3, pp. 82–86, 1995.
18. O. Abu Arqub, M. Al-Smadi, and S. Momani, “Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integrodifferential equations,” Abstract and Applied Analysis, vol. 2012, Article ID 839836, 16 pages, 2012.
19. O. A. Arqub, M. Al-Smadi, and N. Shawagfeh, “Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method,” Applied Mathematics and Computation, vol. 219, no. 17, pp. 8938–8948, 2013.
20. M. Al-Smadi, O. Abu Arqub, and S. Momani, “A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations,” Mathematical Problems in Engineering, vol. 2013, Article ID 832074, 10 pages, 2013.
21. M. Al-Smadi, O. Abu Arqub, and N. Shawagfeh, “Approximate solution of BVPs for 4th-order IDEs by using RKHS method,” Applied Mathematical Sciences, vol. 6, no. 49–52, pp. 2453–2464, 2012.
22. Z. Chen and Y. Lin, “The exact solution of a linear integral equation with weakly singular kernel,” Journal of Mathematical Analysis and Applications, vol. 344, no. 2, pp. 726–734, 2008.
23. M. Cui and Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science Publishers, New York, NY, USA, 2009.