Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method

Physica Scripta

Volumn 75, Issue 6, 2007, Pages 778-787

  Dehghan, Mehdi ^a,b   Shakeri, Fatemeh ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^b INSTITUTE FOR STUDIES IN THEORETICAL PHYSICS AND MATHEMATICS IPM   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; INVERSE PROBLEMS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; THERMAL DIFFUSION;

DIFFUSION EQUATIONS; EMBEDDING PARAMETERS; TEMPERATURE OVERSPECIFICATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 34249315091     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/75/6/007     Document Type: Article

References (40)

1. Hu X B and Wu Y T 1998 Application of the Hirota bilinear for malism to a new integrable differential-difference equation Phys. Lett. A 246 523-9
2. Fan E 2000 Two new applications of the homogeneous balance method Phys. Lett. A 256 353-7
3. Wang M, Zhou Y and Li Z 1996 Applications of a homogeneous balance method to exact solution of nonlinear equations in mathematical physics Phys. Lett. A 216 67-75
4. Vakhnenko V O, Parkes E J and Morrison A J 2003 A Bäcklund transformation and the inverse scattering transform method for the generalized Vakhnenko equation Chaos Solitons Fractals 17 683-92
5. Adomian G and Rach R 1994 Modified decomposition solution of linear and nonlinear boundary-value problems Nonlinear Anal. 23 615-9
6. He J H 1998 Approximate solution of nonlinear differential equations with convolution product nonlinearities Comput. Methods Appl. Mech. Eng. 167 57-68
7. He J H 2006 Some asymptotic methods for strongly nonlinear equations Int. J. Mod. Phys. B 20 1141-99
8. He J 2006 New interpretation of homotopy perturbation method Int. J. Nonlinear Sci. Numer. Simul. 20 2561-8
9. He J H 2006 Homotopy perturbation method for solving boundary value problems Phys. Lett. A 350 87-8
10. Wang Q 2007 Homotopy perturbation method for fractional KdV-Burgers equation Chaos Solitons Fractals at press
11. Cveticanin L 2006 Homotopy perturbation method for pure nonlinear differential equation Chaos Solitons Fractals 30 1221-30
12. Ghasemi M, Tavassoli Kajani M and Babolian E 2007 Application of He's homotopy perturbation method to nonlinear integro-differential equations Appl. Math. Comput. at press
13. Cveticanin L 2005 The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity J. Sound Vibration 285 1171-9
14. Ariel P D, Hayat T and Asghar S 2006 Homotopy perturbation method and axisymmetric flow over a stretching sheet Int. J. Nonlinear Sci. Numer. Simul. 7 399-406
15. Ganj D D and Sadighi A 2006 Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations Int. J. Nonlinear Sci. Numer. Simul. 7 411-8
16. He J H 1999 Homotopy perturbation technique Comput. Methods Appl. Mech. Eng. 178 257-62
17. He J H 2000 A coupling method of a homotopy technique and a perturbation technique for non-linear problems Int. J. Nonlinear Mech. 35 37-43
18. He J H 2003 Homotopy perturbation method: a new nonlinear analytical technique Appl. Math. Comput. 135 73-9
19. He J H 2004 The homotopy perturbation method for nonlinear oscillators with discontinuities Appl. Math. Comput. 151 287-92
20. He J H 2005 Homotopy perturbatin method for nonlinear bifurcation problems Int. J. Nonlinear Sci. Numer. Simul. 6 207-8
21. He J H 2005 Application of homotopy perturbation method to nonlinear wave equations Chaos Solitons Fractals 26 695-700
22. Cannon J R, Lin Y and Xu S 1994 Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations Inverse Problems 10 227-43
23. Cannon J R and Yin H M 1990 Numerical solutions of some parabolic inverse problems Numer. Methods Partial Diff. Eqns 2 177-91
24. Cannon J R and Lin Y 1990 An inverse problem of finding a parameter in a semi-linear heat equation J. Math. Anal. Appl. 145 470-84
25. Cannon J R and Yin H M 1989 On a class of non-classical parabolic problems J. Diff. Eqns. 79 266-88
26. Macbain J A and Bendar J B 1986 Existence and uniqueness properties for one-dimensional inversion problem J. Math. Phys. 27 645-9
27. Prilepko A I and Orlovskii D G 1985 Determination of the evolution parameter of an equation and inverse problems of mathematical physics, I and II J. Diff. Eqns. 21 119-129
28. Wang S Y and Lin A 1989 Finite difference solution to an inverse problem determining a control function in a parabolic partial differential equations Inverse Problems 5 631-40
29. Dehghan M 2001 Determination of a control parameter in the two-dimensional diffusion equation Appl. Numer. Math. 37 489-502
30. Dehghan M 2002 Fourth-order techniques for identifying a control parameter in the parabolic equations Int. J. Eng. Sci. 40 433-47
31. Dehghan M 2003 Numerical solution of one-dimensional parabolic inverse problem Appl. Math. Comput. 136 333-44
32. Dehghan M 2003 Determination of a control function in three-dimensional parabolic equations Math. Comput. Simul. 61 89-100
33. Dehghan M 2000 Finite difference schemes for two-dimensional parabolic inverse problem with energy overspecification Int. J. Comput. Math. 75 339-49
34. Dehghan M 2002 Determination of an unknown parameter in a semi-linear parabolic equation Math. Probl. Eng. 8 111-22
35. Dehghan M 2005 Parameter determination in a partial differential equation from the overspecified data Math. Comput. Modelling 41 196-213
36. Dehghan M 2005 Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement Numer. Methods Partial Diff. Eqns 21 611-22
37. Lin Y 1991 An inverse problem for a class of quasilinear parabolic equations SIAM J. Math. Anal. 22 146-56
38. Dehghan M 2006 Finite difference procedures for solving a problem arising in modelling and design of certain optoelectronic devices Math. Comput. Simul. 71 16-30
39. He J H 1997 A new approach to nonlinear partial differential equations Commun. Nonlinear Sci. Numer. Simul. 2 230-5
40. He J H 2000 Variational iteration method for autonomous ordinary differential systems Appl. Math. Comput. 114 115-23