A new efficient technique for finding the solution of initial-value problems using He's variational iteration method

International Journal for Numerical Methods in Biomedical Engineering

Volumn 27, Issue 9, 2011, Pages 1376-1384

  Tatari, Mehdi ^a  

^a ISFAHAN UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Closed form solution; Initial value problems; Local He's variational iteration method

Indexed keywords

CLOSED FORM SOLUTIONS; EFFICIENT METHOD; LARGE DOMAIN; LARGE REGIONS; VARIATIONAL ITERATION METHOD;

INITIAL VALUE PROBLEMS; PROBLEM SOLVING;

ITERATIVE METHODS;

EID: 80051926378     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1361     Document Type: Article

References (29)

1. He JH. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 2006; 20:1141-1199.
2. He JH. Variational iteration method for autonomous ordinary differential systems. Applied Mathematics and Computations 2000; 114:115-123.
3. Momani S, Abuasad S. Application of He's variational iteration method to Helmholtz equation. Choas, Solitons and Fractals 2006; 27:1119-1123.
4. Abdou MA, Soliman AA. Variational iteration method for solving Burger's and coupled Burger's equations. Journal of Computational and Applied Mathematics 2005; 181:245-251.
5. Inc M. Numerical simulation of KdV and mKdV equations with initial conditions by the variational iteration method. Chaos, Solitons and Fractals 2008; 345:476-484.
6. 1/3 force by He's variational iteration method. Journal of Sound and Vibration 2007; 306:372-376.
7. Momani S, Odibat Z. Analytical approach to linear fractional partial differential equations arising in fluid mechanics. Physics Letters A 2006; 355:271-279.
8. He JH, Wu XH. Construction of solitary solution and compaction-like solution by variational iteration method. Chaos, Solitons and Fractals 2006; 29:108-113.
9. Soliman AA. A numerical simulation and explicit solutions of KdV-Burger's and Lax's seventh-order KdV equations. Chaos, Solitons and Fractals 2006; 29:294-302.
10. Yildirim A, Öziş T. Solutions of singular IVPs of LaneEmden type by the variational iteration method. Nonlinear Analysis 2009; 70:2480-2484.
11. He JH. Variational iteration method-a kind of non-linear analytical technique: some examples. International Journal of Nonlinear Mechanics 1999; 34:699-708.
12. Tatari M, Dehghan M. He's variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation. Chaos, Solitons and Fractals 2007; 33:671-677.
13. Dehghan M, Tatari M. Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method. Chaos, Solitons and Fractals 2008; 36:157-166.
14. Dehghan M, Shakeri S. Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem. Journal of Computational and Applied Mathematics 2008; 214:435-446.
15. Shakeri F, Dehghan M. Numerical solution of a biological population model using He's variational iteration method. Computers and Mathematics with Applications 2007; 54:1197-1209.
16. Shakeri F, Dehghan M. Solution of a model describing biological species living together using the variational iteration method. Mathematical and Computer Modelling 2008; 48:685-699.
17. Tatari M, Dehghan M. On the convergence of He's variational iteration method. Journal of Computational and Applied Mathematics 2007; 207:121-128.
18. He JH, Wu XH. Variational iteration method: new development and applications. Computers and Mathematics with Applications 2007; 54:881-894.
19. He JH. Variational iteration method-some recent results and new interpretations. Journal of Computational and Applied Mathematics 2007; 207:3-17.
20. Ozer H. Application of the variational iteration method to the boundary value problems with jump discontinuities arising in solid mechanics. International Journal of Nonlinear Sciences and Numerical Simulation 2007; 8:513-518.
21. Odibat ZM, Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. International Journal of Nonlinear Sciences and Numerical Simulation 2007; 7:27-34.
22. Yildirim A. Applying He's variational iteration method for solving differential-difference equation. Mathematical Problems in Engineering 2008; 2008 (869614):1-7.
23. Yildirim A. Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations. Communications in Numerical Methods in Engineering 2008; DOI: 10.1002/cnm.1154.
24. Yildirim A. Variational iteration method for inverse problem of diffusion equation. Communications in Numerical Methods in Engineering 2009; DOI: 10.1002/cnm.1258.
25. Koçak H, Yildirim A. Series solution for a delay differential equation arising in electrodynamics. Communications in Numerical Methods in Engineering 2009; DOI: 10.1002/cnm.1288.
26. Ateş İ, Yildirim A. Comparison between variational iteration method and homotopy perturbation method for linear and nonlinear partial differential equations with the nonhomogeneous initial conditions. Numerical Methods for Partial Differential Equations 2009; DOI: 10.1002/num.20511.
27. He JH. Variational iteration method for delay differential equations. Communications in Nonlinear Science and Numerical Simulation 1997; 2:235.
28. He JH. Approximate solution of nonlinear differential equations with convolution product non-linearities. Computer Methods in Applied Mechanics and Engineering 1998; 167:69-73.
29. He JH. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering 1998; 167:57-68.