i ÖZET Bu çalışmanın amacı, homotopi pertürbasyon metodu ve ...

More documents

Recommendations

Info

KAYNAKLAR 141 [1] He J.H, 2006, Non-Perturbative Methods for Strongly nonlinear Problems, dissertation, de -verlag im Internet GmbH, Berlin. [2] He J.H., 2006, Some asymptotic methods for strongly nonlinear equations, Int. J. Modern Phys. B 20(10) 1141-1199. [3] He J.H., 2006, New interpretation of homotopy perturbation method, International Journal of Modern Physics B 20, 2561-2568. [4] He J.H., 2000, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Nonlinear Mech. 35, 37-43. [5] He J.H., 1999, Homotopy perturbation technique, Comp. Meth. Appl. Mech. Eng., 178, 257-262. [6] He J.H., 2005, Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals 26, 695-700. [7] He J.H., 2005, Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simul. 6, 207-208. [8] Ozis T., Agirseven D., 2008, He’s homotopy perturbation method for solving heatlike and wave-like equations with variable coefficients, Phys. Lett. A, 372, 5944-5950. [9] Abbasbandy S., 2006, Numerical solutions of the integral equations: Homotopy perturbation method and Adomian’s decomposition method, Applied Mathematics and Computation, 173, 493-500. [10] Abbasbandy, S., 2006, Application of He’s homotopy perturbation method for Laplace transform, Chaos Solitons & Fractals, 30, 1206-1212. [11] Siddiqui A.M., Ahmed M., Ghori Q.K., 2007, Thin film flow of non-newtonian fluids on a moving belt, Chaos Solitons & Fractals, 33, 1006-1016. [12] Ghori QK, Ahmed M, Siddiqui AM, 2007, Application of homotopy perturbation method to squeezing flow of a Newtonian fluid, International Journal of Nonlinear Sciences and Numerical Simulation, 8 (2): 179-184. [13] Tari H, Ganji DD, Rostamian M, 2007, 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): 203-210.
142 [14] Ghorbani A, Saberi-Nadjafi J, 2007, He's homotopy perturbation method for calculating Adomian polynomials, International Journal of Nonlinear Sciences and Numerical Simulation, 8 (2): 229-232. [15] Ariel PD, Hayat T, Asghar S, 2006, Homotopy perturbation method and axisymmetric flow over a stretching sheet, International Journal of Nonlinear Sciences and Numerical Simulation, 7 (4): 399-406. [16] Ganji DD, Sadighi A, 2006, Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, International Journal of Nonlinear Sciences and Numerical Simulation 7 (4): 411-418. [17] Rafei M, Ganji DD, 2006, Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation 7 (3): 321-328. [18] Siddiqui AM, Mahmood R, Ghori QK, 2006, Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation 7 (1): 7-14. [19] Liao S.J., 2003, Beyond perturbation: Introduction to the homotopy analysis method, Boca Raton:Chapman&Hall/CRC Press. [20] Liao S.J., 1992, A second-order approximate analytical solution of a simple pendulum by the process analysis method, ASME J. Appl. Mech., 59, 970–975. [21] Liao S.J., 1995, An approximate solution technique not depending on small parameters: a special example, Int. J. Non-Linear Mech., 30 (3), 371–380. [22] Liao S.J., 1997, A kind of approximate solution technique which does not depend upon small parameters––II: an application in fluid mechanics, Int. J. Non-Linear Mech. 32(5), 815–822. [23] Liao S.J., 1998, Homotopy analysis method: a new analytic method for nonlinear problems, Appl. Math. Mech. (English-Ed.) 19 (10), 957–962. [24] Liao S.J., 1998, Homotopy analysis method: a new analytical method for nonlinear problems without small parameters, in: The 3rd International Conference on Nonlinear Mechanics, Shanghai, 829–833. [25] Liao S.J., 1999, An explicit totally analytic approximate solution for Blasius viscous flow problem, Int. J. Non-Linear Mech., 34, 759–778. [26] Liao S.J., Chwang AT, 1996, General boundary element method for nonlinear problems, Int.J Numer Meth Fluids, 23, 467-83.
Page 1 and 2:
i ÖZET Bu çalışmanın amacı, h
Page 3 and 4:
iii ÖNSÖZ Bu çalışmanın her a
Page 5 and 6:
v 2.2. Fokker-Planck Denkleminin Ç
Page 7 and 8:
2 analysis method” adlı kitabın
Page 9 and 10:
I. BÖLÜM 4 1. HE’NĐN HOMOTOPĐ
Page 11 and 12:
1.1. Şekil 6 Đlk koşul, H ‘nin
Page 13 and 14:
8 özellikler, pertürbe edilmeyen
Page 15 and 16:
( p) = f ( ) − f ( x ) + pf ( x )
Page 17 and 18:
x n+ 1 veya ( ξ n ) ′ ( ξ ) (
Page 19 and 20:
14 ( ) ( )[ ] ... 6 5 4 3 2 1 5 6 4
Page 21 and 22:
16 rrrr rrrr H v( , p), p) = L( v)
Page 23 and 24:
18 1.2.1. Denklemin çözümü içi
Page 25 and 26:
1.2.2. Isı-tipi modeller 20 Yerkab
Page 27 and 28:
22 p parametresi 1’e yakınsarken
Page 29 and 30:
2 5 x t v 5 ( x, y, t) = , 5! 2 6 y
Page 31 and 32:
Sistem çözülerek v 0 4 4 4 ( x y
Page 33 and 34:
. 2 2 n ∂ vn 1 2 ∂ vn−1 p : =
Page 35 and 36:
2 2 0 ∂ v0 ∂ u0 p : − = 0, 2
Page 37 and 38:
2 t 2 t ( ) = ( + )( − ) + ( −
Page 39 and 40:
34 (1.2.13) denkleminde, p parametr
Page 41 and 42:
1.2.5. Isı-tipi modellerde yakıns
Page 43 and 44:
2 t t için 1+ 2! t 1+ t − e Her
Page 45 and 46:
40 Elde edilen seri çözümün yak
Page 47 and 48:
42 Her [ ] 2 , 0 ∈ t için 1 1804
Page 49 and 50:
4 4 4 3 x y z t v 2 ( x, y, z, t) =
Page 51 and 52:
V3 − u ≤ 3 γ v0 − u bulunur.
Page 53 and 54:
2 3 2 5 3 5 2 x t x t 2 2 t t V2
Page 55 and 56:
50 Elde edilen seri çözümün yak
Page 57 and 58:
52 Her ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∈
Page 59 and 60:
Diferansiyel denklem sisteminden 0
Page 61 and 62:
V 1 3 − u = 1 = = v 1 0 + v 1 1 +
Page 63 and 64:
2 t 2! 3 t 3! 4 t 4! 5 t 5! 2 2 t
Page 65 and 66:
Buradan, lim Vn − u = n→∞ n
Page 67 and 68:
62 denklemi denir. Benzer kısmi di
Page 69 and 70:
( x, t) = 0 v 4 . . . , vn x, t = (
Page 71 and 72:
66 0 p : ∂v0 ∂u0 − = 0, ∂t
Page 73 and 74:
denklem sistemi elde edilir. Başla
Page 75 and 76:
70 Görüldüğü gibi, metot etkin
Page 77 and 78:
72 parametre kullanılır. Bu metot
Page 79 and 80:
Bulunan bu denklemin çözümü: (
Page 81 and 82:
76 seçilen bir iterasyon çarpanı
Page 83 and 84:
Kanıt: 78 (a) Taylor teoremine gö
Page 85 and 86:
Kanıt: (2.1.10) tanımına göre;
Page 87 and 88:
82 ⎧0, m ≤ 1 χ m = ⎨ (2.1.15
Page 89 and 90:
84 ( H ( x, t) ψ N[ φ] ) = H ( x,
Page 91 and 92:
2.1.2.5. Teorem ∈ [ 0, 1] 86 q bi
Page 93 and 94:
88 derece deformasyon denklemine g
Page 95 and 96: 90 r L yardımcı lineer operatör
Page 97 and 98: Kanıt: Eğer seri yakınsak ise s
Page 99 and 100: 94 Liao tarafından kanıtlandığ
Page 101 and 102: 96 (2.2.2) denkleminden, sıfırın
Page 103 and 104: 1.3.2.Örnek için (1.3.3) başlang
Page 105 and 106: u + 3 ( x, t) = −h( 1+ h) 3 h t 2
Page 107 and 108: 102 olarak bulunur. Buradan (2.2.8)
Page 109 and 110: 1.3.4.Örnek için (1.3.6) denklemi
Page 111 and 112: 106 r ∂u ⎡ ∂ ∂ ∂ ∂ ∂
Page 113 and 114: 108 (2.2.11) denkleminden, sıfır
Page 115 and 116: 110 2 2 2 2 2 2 h x t 2 u( x, t) =
Page 117 and 118: 112 h değeri 4.dereceden yaklaşı
Page 119 and 120: 114 h değeri 4.dereceden yaklaşı
Page 121 and 122: 116 Tablolar incelendiğinde ve n =
Page 123 and 124: 118 2.2.Şekil h = −0. 5 için 4.
Page 125 and 126: 120 2.5.Şekil h = −0. 07 için 4
Page 127 and 128: 122 2.8.Şekil h = −0. 03 için 4
Page 129 and 130: 124 Örneğin, h ’nin geçerli b
Page 131 and 132: 126 2.14.Şekil h = −0. 09 için
Page 133 and 134: 1.3.5.Örnek için: app xxt 2 3 4 (
Page 135 and 136: 130 geçerli bölgesinden h = −1
Page 137 and 138: 132 yaklaşık çözümlerinin de
Page 139 and 140: 134 h ’nin geçerli bölgesinden
Page 141 and 142: 136 olduğu görülür. Yine her ik
Page 143 and 144: 138 3.5.a. Şekil HAM ile bulunan h
Page 145: 140 iken homotopi pertürbasyon met
Page 149 and 150: 144 [42] Sajid M., Hayat T., 2009,
Page 151: KĐŞĐSEL BĐLGĐLER Adı Soyadı
show all

i ÖZET Bu çalışmanın amacı, homotopi pertürbasyon metodu ve ...

Create successful ePaper yourself

Delete template?

Save as template?