Application of reproducing kernel method for solving nonlinear fredholm-volterra integrodifferential equations

Abstract and Applied Analysis

Volumn 2012, Issue , 2012, Pages

  Abu Arqub, Omar ^a   Al Smadi, Mohammed ^b   Momani, Shaher ^c  

^a AL BALQA APPLIED UNIVERSITY   (Jordan)

^b TAFILA TECHNICAL UNIVERSITY   (Jordan)

^c UNIVERSITY OF JORDAN   (Jordan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867025265     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2012/839836     Document Type: Article

References (30)

1. Bloom F., Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory. Journal of Mathematical Analysis and Applications 1980 73 2 524 542 10.1016/0022-247X(80) 90297-8 564002
2. Holmåker K., Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones. SIAM Journal on Mathematical Analysis 1993 24 1 116 128 10.1137/0524008 1199530 ZBL0767.45005
3. Forbes L. K., Crozier S., Doddrell D. M., Calculating current densities and fields produced by shielded magnetic resonance imaging probes. SIAM Journal on Applied Mathematics 1997 57 2 401 425 10.1137/S0036139995283110 1438760 (Pubitemid 127577098)
4. Kanwal R. P., Linear Integral Differential Equations Theory and Technique 1971 New York, NY, USA Academic Press
5. Maleknejad K., Mahmoudi Y., Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations. Applied Mathematics and Computation 2003 145 2-3 641 653 10.1016/S0096-3003(03)00152-8 2009290 ZBL1032.65144
6. Babolian E., Masouri Z., Hatamzadeh-Varmazyar S., Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions. Computers and Mathematics with Applications 2009 58 2 239 247 10.1016/j.camwa.2009.03.087 2535790 ZBL1189.65306
7. Babolian E., Masouri Z., Hatamzadeh-Varmazyar S., New direct method to solve nonlinear Volterra-Fredholm integral and integro-differential equations using operational matrix with block-pulse functions. Progress In Electromagnetics Research B 2008 8 59 76
8. Maleknejad K., Basirat B., Hashemizadeh E., Hybrid Legendre polynomials and block-pulse functions approach for nonlinear Volterra-Fredholm integro-differential equations. Computers and Mathematics with Applications 2011 61 9 2821 2828 10.1016/j.camwa.2011.03.055 2795406 ZBL1221.65333
9. Momani S., Qaralleh R., An efficient method for solving systems of fractional integro-differential equations. Computers and Mathematics with Applications 2006 52 3-4 459 470 10.1016/j.camwa.2006.02.011 2263514 ZBL1137.65072 (Pubitemid 44648715)
10. Ghasemi M., Tavassoli Kajani M., Babolian E., Application of He's homotopy perturbation method to nonlinear integro-differential equations. Applied Mathematics and Computation 2007 188 1 538 548 10.1016/j.amc.2006.10.016 2327381 ZBL1118.65394 (Pubitemid 46705451)
11. El-Ajou A., Abu Arqub O., Momani S., Homotopy analysis method for second-order boundary value problems of integro-differential equations. Discrete Dynamics in Nature and Society. In press
12. Berlinet A., Thomas-Agnan C., Reproducing Kernel Hilbert Space in Probability and Statistics 2004 Boston, Mass, USA Kluwer Academic 10.1007/978-1-4419-9096-9 2239907
13. Cui M., Lin Y., Nonlinear Numercial Analysis in the Reproducing Kernel Space 2008 New York, NY, USA Nova Science
14. Daniel A., Reproducing Kernel Spaces and Applications 2003 New York, NY, USA Springer
15. Cui M., Du H., Representation of exact solution for the nonlinear Volterra-Fredholm integral equations. Applied Mathematics and Computation 2006 182 2 1795 1802 10.1016/j.amc.2006.06.016 2282621 ZBL1110.45005 (Pubitemid 44841977)
16. Du H., Shen J., Reproducing kernel method of solving singular integral equation with cosecant kernel. Journal of Mathematical Analysis and Applications 2008 348 1 308 314 10.1016/j.jmaa.2008.07.037 2449348 ZBL1152.45007
17. Geng F., A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems. Applied Mathematics and Computation 2009 213 1 163 169 10.1016/j.amc.2009.02.053 2533372 ZBL1166.65358
18. Geng F., Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method. Applied Mathematics and Computation 2009 215 6 2095 2102 10.1016/j.amc.2009.08.002 2557093 ZBL1178.65085
19. Geng F., Cui M., Solving singular nonlinear two-point boundary value problems in the reproducing kernel space. Journal of the Korean Mathematical Society 2008 45 3 631 644 10.4134/JKMS.2008.45.3.631 2410235 ZBL1154.34012
20. Geng F., Cui M., Solving a nonlinear system of second order boundary value problems. Journal of Mathematical Analysis and Applications 2007 327 2 1167 1181 10.1016/j.jmaa.2006.05.011 2279996 ZBL1113.34009 (Pubitemid 44742807)
21. Geng F., Cui M., Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space. Applied Mathematics and Computation 2007 192 2 389 398 10.1016/j.amc.2007.03.016 2385604 ZBL1193.34017 (Pubitemid 47445700)
22. Li J., A computational method for solving singularly perturbed two-point singular boundary value problem. International Journal of Mathematical Analysis 2008 2 21-24 1089 1096 2514971 ZBL1167.65043
23. Li C.-l., Cui M.-g., The exact solution for solving a class nonlinear operator equations in the reproducing kernel space. Applied Mathematics and Computation 2003 143 2-3 393 399 10.1016/S0096-3003(02)00370-3 1981704 ZBL1034.47030
24. Li Y., Geng F., Cui M., The analytical solution of a system of nonlinear differential equations. International Journal of Mathematical Analysis 2007 1 9-12 451 462 2340087 ZBL1130.34300
25. Lin Y. Z., Cui M. G., Yang L. H., Representation of the exact solution for a kind of nonlinear partial differential equation. Applied Mathematics Letters 2006 19 8 808 813 10.1016/j.aml.2005.10.010 2232259 ZBL1116.35309
26. Lü X., Cui M., Solving a singular system of two nonlinear ODEs. Applied Mathematics and Computation 2008 198 2 534 543 10.1016/j.amc.2007.08.054 2405956 ZBL1152.65077 (Pubitemid 351400728)
27. Yang L., Cui M., New algorithm for a class of nonlinear integro-differential equations in the reproducing kernel space. Applied Mathematics and Computation 2006 174 2 942 960 10.1016/j.amc.2005.05.026 2220590 ZBL1094.65136
28. Lin Y., Chung P., Cui M., A solution of an infinite system of quadratic equations in reproducing kernel space. Complex Analysis and Operator Theory 2007 1 4 571 579 10.1007/s11785-007-0019-9 2358012 ZBL1136.46024
29. Al-Smadi M., Abu Arqub O., Shawagfeh N., Approximate solution of BVPs for 4th-order IDEs by using RKHS method. Applied Mathematical Sciences 2012 6 2453 2464
30. Zhou Y., Cui M., Lin Y., Numerical algorithm for parabolic problems with non-classical conditions. Journal of Computational and Applied Mathematics 2009 230 2 770 780 10.1016/j.cam.2009.01.012 2536006 ZBL1190.65136