Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method

Applied Mathematics and Computation

Volumn 219, Issue 17, 2013, Pages 8938-8948

  Arqub, Omar Abu ^a   Al Smadi, Mohammed ^b   Shawagfeh, Nabil ^a  

^a AL BALQA APPLIED UNIVERSITY   (Jordan)

^b TAFILA TECHNICAL UNIVERSITY   (Jordan)

Author keywords

Exact solution; Fredholm integro differential equation; Reproducing kernel Hilbert space

Indexed keywords

APPROXIMATE SOLUTION; EXACT SOLUTION; FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS; INITIAL CONDITIONS; NUMERICAL RESULTS; NUMERICAL SOLUTION; REPRODUCING KERNEL HILBERT SPACES;

DIFFERENTIAL EQUATIONS; ITERATIVE METHODS; NUMERICAL METHODS;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 84876575020     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.03.006     Document Type: Article

References (32)

1. F. Bloom Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory J. Math. Anal. Appl. 73 1980 524 542
2. K. Holmaker Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones SIAM J. Math. Anal. 24 1993 116 128
3. L.K. Forbes, S. Crozier, and D.M. Doddrell Calculating current densities and fields produced by shielded magnetic resonance imaging probes SIAM J. Appl. Math. 57 1997 401 425 (Pubitemid 127577098)
4. R.P. Kanwal Linear Integral Differential Equations Theory and Technique 1971 Academic Press New York
5. K. Maleknejad, and M. Attary An efficient numerical approximation for the linear class of Fredholm integro-differential equations based on Cattani's method Commun. Nonlinear Sci. Numer. Simul. 16 2011 2672 2679
6. M.Y. Rahimi-Ardabili, and S. Shahmorad Iterative numerical solution of non-linear integro-differential equations by the Tau method Appl. Math. Comput. 193 2007 514 522 (Pubitemid 350001202)
7. H. Jaradat, O. Alsayyed, and S. Al-Shara Numerical solution of linear integro-differential equations J. Math. Stat. 4 2008 250 254
8. P. Darania, and A. Ebadian A method for the numerical solution of the integro-differential equations Appl. Math. Comput. 188 2007 657 668 (Pubitemid 46686756)
9. J. Rashidinia, and M. Zarebnia The numerical solution of integro-differential equation by means of the Sinc method Appl. Math. Comput. 188 2007 1124 1130 (Pubitemid 46722628)
10. M. Ghasemi, M.T. Kajani, and E. Babolian Application of He's homotopy perturbation method to nonlinear integro-differential equations Appl. Math. Comput. 188 2007 538 548 (Pubitemid 46705451)
11. M.I. Berenguer, M.V.F. Muñoz, A.I. Garralda-Guillem, and M.R. Galán A sequential approach for solving the Fredholm integro-differential equation Appl. Numer. Math. 62 2012 297 304
12. A. Berlinet, and C. Thomas-Agnan Reproducing Kernel Hilbert Space in Probability and Statistics 2004 Kluwer Academic Publishers
13. M. Cui, and Y. Lin Nonlinear Numercial Analysis in the Reproducing Kernel Space 2008 Nova Science Publisher New York
14. A. Daniel Reproducing Kernel Spaces and Applications 2003 Springer
15. F. Geng Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method Appl. Math. Comput. 215 2009 2095 2102
16. F. Geng, and M. Cui Solving singular nonlinear two-point boundary value problems in the reproducing kernel space J. Korean Math. Soc. 45 2008 631 644
17. F. Geng, and M. Cui Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space Appl. Math. Comput. 192 2007 389 398 (Pubitemid 47445700)
18. F. Geng, and M. Cui Solving a nonlinear system of second order boundary value problems J. Math. Anal. Appl. 327 2007 1167 1181 (Pubitemid 44742807)
19. Y. Lin, M. Cui, and L. Yang Representation of the exact solution for a kind of nonlinear partial differential equations Appl. Math. Lett. 19 2006 808 813
20. Y. Zhoua, M. Cui, and Y. Lin Numerical algorithm for parabolic problems with non-classical conditions J. Comput. Appl. Math. 230 2009 770 780
21. M. Cui, and H. Du Representation of exact solution for the nonlinear Volterra-Fredholm integral equations Appl. Math. Comput. 182 2006 1795 1802 (Pubitemid 44841977)
22. H. Du, and J. Shen Reproducing kernel method of solving singular integral equation with cosecant kernel J. Math. Anal. Appl. 348 2008 308 314
23. O. Abu Arqub, M. Al-Smadi, and S. Momani Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integro-differential equations Abstr. Appl. Anal. vol. 2012 2012 pp. 16 10.1155/2012/839836 (Article ID 839836)
24. M. Al-Smadi, O. Abu Arqub, N. Shawagfeh, S. Momani, A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations, Mathematical Problems in Engineering, Volume 2013, Article ID 832074, pp. 10. .
25. C. Li, and M. Cui The exact solution for solving a class nonlinear operator equations in the reproducing kernel space Appl. Math. Comput. 143 2003 393 399
26. Y. Lin, P. Chung, and M. Cui A solution of an infinite system of quadratic equations in reproducing kernel space Complex Anal. Oper. Theory 1 2007 571 579
27. Y. Lin, M. Cui, and Y. Zheng Representation of the exact solution for infinite system of linear equations Appl. Math. Comput. 168 2005 636 650
28. L.H. Yang, and Y. Lin Reproducing kernel methods for solving linear initial-boundary-value problems Electron. J. Differ. Eqs. 2008 2008 1 11
29. H. Danfu, and S. Xufeng Numerical solution of integro-differential equations by using CAS wavelet operational matrix of integration Appl. Math. Comput. 194 2007 460 466 (Pubitemid 350088986)
30. M. Ghasemi, M.T. Kajani, and E. Babolian Application of He's homotopy perturbation method to nonlinear integro-differential equations Appl. Math. Comput. 188 2007 538 548 (Pubitemid 46705451)
31. P. Darania, and A. Ebadian Development of the Taylor expansion approach for nonlinear integro-differential equations Int. J. Contemp. Math. Sci. 1 2006 651 664
32. N. Aghazadeh, and H. Mesgarani Solving non-linear Fredholm integro-differential equations World Appl. Sci. J. 7 2009 50 56