Homotopy analysis method for second-order boundary value problems of integrodifferential equations

Discrete Dynamics in Nature and Society

Volumn 2012, Issue , 2012, Pages

  El Ajou, Ahmad ^a   Abu Arqub, Omar ^a   Momani, Shaher ^b  

^a AL BALQA APPLIED UNIVERSITY   (Jordan)

^b UNIVERSITY OF JORDAN   (Jordan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867790334     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2012/365792     Document Type: Article

References (31)

1. Kanwal R. P., Linear Integral Differential Equations: Theory and Technique 1996 2nd Boston, Ga, USA Birkhauser ZBL0855.34062
2. 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
3. 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
4. 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)
5. Jerri A. J., Introduction to Integral Equations with Applications 1999 2nd New York, NY, USA John Wiley & Sons 1800272
6. Agarwal R. P., Boundary value problems for higher order integro-differential equations. Nonlinear Analysis 1983 7 3 259 270 10.1016/0362-546X(83)90070-6 693443 ZBL0505.45002
7. Agarwal R. P., Boundary Value Problems for High Ordinary Differential Equations 1986 Singapore World Scientific 1021979
8. Wang Z., Liu L., Wu Y., The unique solution of boundary value problems for nonlinear second-order integral-differential equations of mixed type in Banach spaces. Computers & Mathematics with Applications 2007 54 9-10 1293 1301 10.1016/j.camwa.2007.04.018 2397681 ZBL1156.34051 (Pubitemid 47576573)
9. Saadatmandi A., Dehghan M., Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients. Computers & Mathematics with Applications 2010 59 8 2996 3004 10.1016/j.camwa.2010.02.018 2608006 ZBL1193.65229
10. Zhao J., Corless R. M., Compact finite difference method for integro-differential equations. Applied Mathematics & Computation 2006 177 1 271 288 10.1016/j.amc.2005.11.007 2234518 ZBL1102.65144 (Pubitemid 43815532)
11. Al-Mdallal Q. M., Monotone iterative sequences for nonlinear integro-differential equations of second order. Nonlinear Analysis 2011 12 6 3665 3673 10.1016/j.nonrwa.2011.06.023 2833000 ZBL1231.45016
12. Liao S. J., Beyond Perturbation: Introduction to the Homotopy Analysis Methods 2003 Boca Raton, Fla, USA Chapman & Hall 2058313
13. Liao S., On the homotopy analysis method for nonlinear problems. Applied Mathematics & Computation 2004 147 2 499 513 10.1016/S0096-3003(02)00790-7 2012589 ZBL1086.35005
14. Liao S. J., Homotopy analysis method: a new analytic method for nonlinear problems. Applied Mathematics & Mechanics 1998 19 10 957 962 10.1007/BF02457955 1675887 ZBL1126.34311
15. Liao S. J., Cheung K. F., Homotopy analysis of nonlinear progressive waves in deep water. Journal of Engineering Mathematics 2003 45 2 105 116 10.1023/A:1022189509293 1958069 ZBL1112.76316 (Pubitemid 36352562)
16. Liao S., Series solutions of unsteady boundary-layer flows over a stretching flat plate. Studies in Applied Mathematics 2006 117 3 239 263 10.1111/j.1467-9590.2006.00354.x 2257099 ZBL1145.76352 (Pubitemid 44327609)
17. Wu W., Liao S. J., Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons and Fractals 2005 26 1 177 185 2-s2.0-17644421077 10.1016/j.chaos.2004.12.016 ZBL1071.76009 (Pubitemid 40556381)
18. Sun Q., Solving the Klein-Gordon equation by means of the homotopy analysis method. Applied Mathematics & Computation 2005 169 1 355 365 10.1016/j.amc.2004.09.056 2171153 ZBL1078.35105 (Pubitemid 41491859)
19. Yabushita K., Yamashita M., Tsuboi K., An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method. Journal of Physics A 2007 40 29 8403 8416 10.1088/1751-8113/40/29/015 2371242
20. Zurigat M., Momani S., Odibat Z., Alawneh A., The homotopy analysis method for handling systems of fractional differential equations. Applied Mathematical Modelling 2010 34 1 24 35 10.1016/j.apm.2009.03.024 2566678 ZBL1185.65140
21. Odibat Z., Momani S., Xu H., A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations. Applied Mathematical Modelling 2010 34 3 593 600 10.1016/j.apm.2009.06.025 2563341 ZBL1185.65139
22. Hashim I., Abdulaziz O., Momani S., Homotopy analysis method for fractional IVPs. Communications in Nonlinear Science and Numerical Simulation 2009 14 3 674 684 10.1016/j.cnsns.2007.09.014 2449879 ZBL1221.65277
23. Zurigat M., Momani S., Alawneh A., Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy analysis method. Computers & Mathematics with Applications 2010 59 3 1227 1235 10.1016/j.camwa.2009.07.002 2579484 ZBL1189.65187
24. Arqub O. Abu, El-Ajou A., Solution of the fractional epidemic model by homotopy analysis method. Journal of King Saud University. In press
25. Vosughi H., Shivanian E., Abbasbandy S., A new analytical technique to solve Volterra's integral equations. Mathematical Methods in the Applied Sciences 2011 34 10 1243 1253 10.1002/mma.1436 2838775 ZBL1239.65084
26. Nik H. S., Effati S., Buzhabadi R., Analytic-approximate solution for an integro-differential equation arising in oscillating magnetic fields using homotopy analysis method. Iranian Journal of Optimization 2010 2 3 518 535
27. Khan N. A., Ara A., Jamil M., Approximations of the nonlinear Volterra's population model by an efficient numerical method. Mathematical Methods in the Applied Sciences 2011 34 14 1733 1738 10.1002/mma.1479 2833826 ZBL1223.92047
28. Zurigat M., Momani S., Alawneh A., Homotopy analysis method for systems of fractional integro-differential equations. Neural, Parallel & Scientific Computations 2009 17 2 169 186 2588351 ZBL1180.65181
29. Jaradat H. M., Awawdeh F., Alsayyed O., Series solution to the high-order integro-differential equations. Analele Universitaii din OradeaFascicola Matematica 2009 16 247 257. Tom XVI 2541660 ZBL1199.65420
30. Cang J., Tan Y., Xu H., Liao S. J., Series solutions of non-linear Riccati differential equations with fractional order. Chaos, Solitons and Fractals 2009 40 1 1 9 10.1016/j.chaos.2007.04.018 2517912 ZBL1197.34006
31. Allan F. M., Derivation of the Adomian decomposition method using the homotopy analysis method. Applied Mathematics & Computation 2007 190 1 6 14 10.1016/j.amc.2006.12.074 2335425 ZBL1125.65063 (Pubitemid 46856640)