The variational iteration method: A highly promising method for solving the system of integro-differential equations

Computers and Mathematics with Applications

Volumn 56, Issue 2, 2008, Pages 346-351

  Saberi Nadjafi, Jafar ^a   Tamamgar, Mohamadreza ^a  

^a FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

Author keywords

Approximate solution; Integro differential equation; System; Variational iteration method; Volterra

Indexed keywords

APPROXIMATION THEORY; ITERATIVE METHODS; NONLINEAR EQUATIONS; VARIATIONAL TECHNIQUES;

APPROXIMATE SOLUTION; VARIATIONAL ITERATION METHOD;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 44149091947     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2007.12.014     Document Type: Article

References (24)

1. Wang H., Fu H.M., Zhang H.F., et al. A practical thermodynamic method to calculate the best glass-forming composition for bulk metallic glasses. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 171-178
2. Xu L., He J.H., and Liu Y. Electrospun nanoporous spheres with Chinese drug. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 199-202
3. Sun F.Z., Gao M., Lei S.H., et al. The fractal dimension of the fractal model of dropwise condensation and its experimental study. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 211-222
4. Bo T.L., Xie L., and Zheng X.J. Numerical approach to wind ripple in desert. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 223-228
5. El-Shahed M. Application of He's homotopy perturbation method to Volterra's integro-differential equation. International Journal of Nonlinear Sciences and Numerical Simulation 6 2 (2005) 163-168
6. El-Sayed S.M., Kaya D., and Zarea S. The decomposition method applied to solve high-order linear Volterra-Fredholm integro-differential equations. International Journal of Nonlinear Sciences and Numerical Simulation 5 2 (2004) 105-112
7. He J.H. Variational iteration method - a kind of non-linear analytical technique: Some examples. International Journal of Non-linear Mechanics 34 4 (1999) 699-708
8. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering 167 1-2 (1998) 57-68
9. He J.H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 20 10 (2006) 1141-1199
10. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons and Fractals 29 1 (2006) 108-113
11. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. International Journal of Nonlinear Sciences and Numerical Simulation 7 1 (2006) 27-34
12. Bildik N., and Konuralp A. The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations. International Journal of Nonlinear Sciences and Numerical Simulation 7 1 (2006) 65-70
13. Yusufoglu E. Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 153-158
14. Tari H., Ganji D.D., and Rostamian M. Approximate solutions of K (2,2), KdV and modified KdV equations by variational iteration method, homotopy perturbation method and homotopy analysis method. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 203-210
15. Bildik N., and Konuralp A. Two-dimensional differential transform method, Adomian's decomposition method, and variational iteration method for partial differential equations. International Journal of Computer Mathematics 83 12 (2006) 973-987
16. Da-Hua Shou, Ji-Huan He, Beyond Adomian method: The variational iteration method for solving heat-like and wave-like equations with variable coefficients, Physics Letters A, doi:10.1016/j.physleta.2007.07.011
17. Xu L., He J.-H., and Wazwaz A.-M. Variational iteration method-reality, potential, and challenges. Journal of Computational and Applied Mathematics 207 1 (2007) 1-2
18. Ji-Huan He, Abdul-Majid Wazwaz, Lan Xu, The variational iteration method: Reliable, efficient, and promising, Computers & Mathematics with Applications, doi:10.1016/j.camwa.2006.12.056
19. Shu-Qiang W., and Ji-Huan H. Variational iteration method for solving integro-differential equations. Physics Letters A 367 3 (2007) 188-191
20. Lan Xu, Variational iteration method for solving integral equations, International Journal of Computer and Mathematics with Applications, doi:10.1016/j.camwa.2006.12.053
21. N.H. Sweilam, Fourth order integro-differential equations using variational iteration method, Computers and Mathematics with Applications, doi:10.1016/j.camwa.2006.12.055
22. Yusufoglu E. An efficient algorithm for solving inegro-differential equations system. Applied Mathematics and Computation 192 1 (2007) 51-55
23. He J.-H. Variational approach for nonlinear oscillators. Chaos, Solitons and Fractals 34 5 (2007) 1430-1439
24. He J.-H. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons and Fractals 19 4 (2004) 847-851