A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations

Mathematical Problems in Engineering

Volumn 2013, Issue , 2013, Pages

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

^a TAFILA TECHNICAL UNIVERSITY   (Jordan)

^b AL BALQA APPLIED UNIVERSITY   (Jordan)

^c UNIVERSITY OF JORDAN   (Jordan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE SOLUTION; COMPUTABLE COMPONENTS; CONVERGENT SERIES; FOURTH-ORDER; REPRODUCING KERNEL HILBERT SPACES; TWO-POINT BOUNDARY VALUE PROBLEM;

INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL TECHNIQUES;

BOUNDARY VALUE PROBLEMS;

EID: 84877937374     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2013/832074     Document Type: Article

References (27)

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 MR564002
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 MR1199530 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 MR1438760 (Pubitemid 127577098)
4. Kanwal R. P., Linear Integral differential Equations Theory and Technique 1971 New York, NY, USA Academic Press
5. Wazwaz A.-M., A reliable algorithm for solving boundary value problems for higher-order integro-differentiable equations. Applied Mathematics and Computation 2001 118 2-3 327 342 10.1016/S0096-3003(99)00225-8 MR1812962 ZBL1023.65150 (Pubitemid 33592924)
6. Arikoglu A., Ozkol I., Solution of boundary value problems for integro-differential equations by using differential transform method. Applied Mathematics and Computation 2005 168 2 1145 1158 10.1016/j.amc.2004.10.009 MR2171768 ZBL1090.65145 (Pubitemid 41405667)
7. Yildirim A., Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method. Computers & Mathematics with Applications 2008 56 12 3175 3180 10.1016/j.camwa.2008.07.020 MR2474572 ZBL1165.65377
8. Saeidy M., Matinfar M., Vahidi J., Analytical solution of BVPs for fourth-order integro-differential equations by using homotopy analysis method. International Journal of Nonlinear Science 2010 9 4 414 421 MR2670955
9. Abu Arqub O., Series solution of fuzzy differential equations under strongly generalized di erentiability. Journal of Advanced Research in Applied Mathematics 2013 5 31 52
10. Abu Arqub O., El-Ajou A., Momani S., Shawagfeh N., Analytical solutions of fuzzy initial value problems by HAM. Applied Mathematics and Information Sciences. In press
11. Abu Arqub O., El-Ajou A., Solution of the fractional epidemic model by homotopy analysis method. Journal of King Saud University (Science) 2013 25 73 81
12. Momani S., Qaralleh R., An efficient method for solving systems of fractional integro-differential equations. Journal of Mathematical Analysis and Applications 2006 52 3-4 459 470 10.1016/j.camwa.2006.02.011 (Pubitemid 44648715)
13. 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 2012 2012 18 365792 10.1155/2012/365792
14. Abu Arqub O., Abo-Hammour Z., Momani S., Application of continuous genetic algorithm for nonlinear system of second-order boundary value problems. Applied Mathematics and Information Sciences. In press
15. Abu Arqub O., Abo-Hammour Z., Momani S., Shawagfeh N., Solving singular two-point boundary value problems using continuous genetic algorithm. Abstract and Applied Analysis 2012 2012 25 205391 10.1155/2012/205391
16. Berlinet A., Thomas-Agnan C., Reproducing Kernel Hilbert Spaces in Probability and Statistics 2004 Boston, Mass, USA Kluwer Academic Publishers xxii+355 10.1007/978-1-4419-9096-9 MR2239907
17. Cui M., Lin Y., Nonlinear Numerical Analysis in the Reproducing Kernel Space 2009 New York, NY, USA Nova Science xiv+226 MR2502102
18. Alpay D., Reproducing Kernel Spaces and Applications 2003 143 Basel, Switzerland Birkhäuser xvi+344 Operator Theory: Advances and Applications 10.1007/978-3-0348-8077-0 MR2019345
19. 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 MR1981704 ZBL1034.47030
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 MR2279996 ZBL1113.34009 (Pubitemid 44742807)
21. 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 MR2533372 ZBL1166.65358
22. 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 MR2340087 ZBL1130.34300
23. 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 MR2557093 ZBL1178.65085
24. 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 MR2232259 ZBL1116.35309
25. 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 MR2282621 ZBL1110.45005 (Pubitemid 44841977)
26. 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 49-52 2453 2464 MR2912763
27. Abu Arqub O., Al-Smadi M., Momani S., Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integrodifferential equations. Abstract and Applied Analysis 2012 16 839836 MR2969993 ZBL1253.65200