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

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143 [27] Liao S.J., 1997, General boundary element method for nonlinear heat transfer problems governed by hyperbolic heat conduction equation, Comput.Mech., 20(5), 397- 406. [28] Liao S.J., 1999, On the general boundary element method and its further generalization, Int J. Numer Meth Fluids , 31, 627-55. [29] Liao S.J., 1999, A uniformly valid analytic solution of two dimensional viscous flow over a semiinfinite flat plate, J. Fluid Mech. 385, 101–128. [30] Liao S.J., 2001, A non-iterative numerical approach for 2-D viscous flow problems governed by the Falkner–Skan equation, Int. J. Numer. Methods Fluids 35 (5), 495–518. [31] Liao S.J., 2009, “Notes on the homotopy analysis method: Some definitions and theorems”, Commun Nonlinear Sci Numer Simulat, 14, 983-997. [32] Song H, Tao L., 2007, Homotopy analysis of 1D unsteady, nonlinear groundwater flow through porous media. J Coastal Res ., 50, 292–295. [33] Molabahrami A, Khani F., 2009, The homotopy analysis method to solve the Burgers–Huxley equation. Nonlinear Anal B: Real World Appl, 10,2,589-600. [34] Bataineh AS, Noorani MSM, Hashim I., 2007, Solutions of time-dependent Emden–Fowler type equations by homotopy analysis method. Phys Lett A, 371:72–82. [35] Wang Z, Zou L, Zhang H., 2007, Applying homotopy analysis method for solving differential-difference equation. Phys Lett A , 369, 77–84. [36] Mustafa Inc., 2007, On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method. Phys Lett A, 365, 412–15. [37] Abbasbandy S., 2006, “The application of the homotopy analysis method to nonlinear equations arising in heat transfer”, Physics Letters A, 360, 109-113. [38] Abbasbandy S., 2007, “The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation”, Physics Letters A, 361, 478-483. [39] He J.H., 2004, Comparison of homotopy perturbation method and homotopy analysis method, Applied Mathematics and Computation, 156(2), 527-539. [40] Liao S.J., 2005, Comparison between the homotopy analysis method and homotopy perturbation method, Appl. Math. Comput., 169, 1186–1194. [41] Sajid M., Hayat T., 2008, Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations, Nonlinear Analysis: Real World Applications, 9, 2296-2301.
144 [42] Sajid M., Hayat T., 2009, Comparison of HAM and HPM solutions in heat radiation equations, Int. Communications in Heat and Mass Transfer, 36, 59-62. [43] Liang S., Jeffrey D.J., 2009, Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation, Commun. Nonliner. Sci. Numer. Simulat., doi:10.1016/j.cnsns.2009.02.016. [44] Biazar J., Hosseini K., Gholamin P., 2008, Homotopy Perturbation Method Fokker- Planck Equation, International Mathematical Forum, 3-19, 945-954. [45] Gray B., 1975, Homotopy Theory: An Introduction to Algebraic Topology Academic Pr , ISSN: 0122960505. [46] Cropper A., William H., 2004, Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking, Oxford University Press, p.34, ISBN 978-0-19- 517324-6. [47] He,J.H., Newton-like iteration method for solving algebraic equations, 1998, Commun. Nonlinear Sci. Numer. Simulat., 3 (2), 106–109. [48] Javidi M., 2007, Iterative methods to nonlinear equations, Applied Mathematics and Computation, 193, 360-365. [49] Holliday JR, Rundle JB, Tiampo KF, et al, 2006, Modification of the pattern informatics method for forecasting large earthquake events using complex eigenfactors Tectonophysics, 413 ,1-2, 87-91. [50] Akhmetov AA, 2003, Long current loops as regular solutions of the equation for coupling currents in a flat two-layer superconducting cable Cryogenics, 43, 3-5, 317- 322. [51] Manolis GD, Rangelov TV, 2006, Non-homogeneous elastic waves in soils: Notes on the vector decomposition technique, Soil Dynamics and Earthquake Engineering, 26, 952-959. [52] Nochetto RH, Pyo JH, 2005, Error estimates for semi-discrete gauge methods for the Navier-Stokes equations Mathematics of Computation 74, 521-542. [53] Wazwaz AM, Gorguis A, 2004, Exact solutions for heat-like and wave-like equations with variable coefficients, Applied Mathematics and Computation, 149,1, 15- 29. [54] Momani S, 2005, Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method Applied Mathematics and Computation, 165, 2, 459-472 [55] Shou D.H, He J.H., 2008, Beyond Adomian method: The variational iteration method for solving heat-like and wave-like equations with variable coefficients, Phys. Lett. A 372 (3), 233–237.
Page 1 and 2:
i ÖZET Bu çalışmanın amacı, h
Page 3 and 4:
iii ÖNSÖZ Bu çalışmanın her a
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v 2.2. Fokker-Planck Denkleminin Ç
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2 analysis method” adlı kitabın
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I. BÖLÜM 4 1. HE’NĐN HOMOTOPĐ
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1.1. Şekil 6 Đlk koşul, H ‘nin
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8 özellikler, pertürbe edilmeyen
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( p) = f ( ) − f ( x ) + pf ( x )
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x n+ 1 veya ( ξ n ) ′ ( ξ ) (
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14 ( ) ( )[ ] ... 6 5 4 3 2 1 5 6 4
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16 rrrr rrrr H v( , p), p) = L( v)
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18 1.2.1. Denklemin çözümü içi
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1.2.2. Isı-tipi modeller 20 Yerkab
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22 p parametresi 1’e yakınsarken
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2 5 x t v 5 ( x, y, t) = , 5! 2 6 y
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Sistem çözülerek v 0 4 4 4 ( x y
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. 2 2 n ∂ vn 1 2 ∂ vn−1 p : =
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2 2 0 ∂ v0 ∂ u0 p : − = 0, 2
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2 t 2 t ( ) = ( + )( − ) + ( −
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34 (1.2.13) denkleminde, p parametr
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1.2.5. Isı-tipi modellerde yakıns
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2 t t için 1+ 2! t 1+ t − e Her
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40 Elde edilen seri çözümün yak
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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.
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2 3 2 5 3 5 2 x t x t 2 2 t t V2
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50 Elde edilen seri çözümün yak
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52 Her ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∈
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Diferansiyel denklem sisteminden 0
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V 1 3 − u = 1 = = v 1 0 + v 1 1 +
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2 t 2! 3 t 3! 4 t 4! 5 t 5! 2 2 t
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Buradan, lim Vn − u = n→∞ n
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62 denklemi denir. Benzer kısmi di
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( x, t) = 0 v 4 . . . , vn x, t = (
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66 0 p : ∂v0 ∂u0 − = 0, ∂t
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denklem sistemi elde edilir. Başla
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70 Görüldüğü gibi, metot etkin
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72 parametre kullanılır. Bu metot
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Bulunan bu denklemin çözümü: (
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76 seçilen bir iterasyon çarpanı
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Kanıt: 78 (a) Taylor teoremine gö
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Kanıt: (2.1.10) tanımına göre;
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82 ⎧0, m ≤ 1 χ m = ⎨ (2.1.15
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84 ( H ( x, t) ψ N[ φ] ) = H ( x,
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2.1.2.5. Teorem ∈ [ 0, 1] 86 q bi
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88 derece deformasyon denklemine g
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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 and 146: 140 iken homotopi pertürbasyon met
Page 147: 142 [14] Ghorbani A, Saberi-Nadjafi
Page 151: KĐŞĐSEL BĐLGĐLER Adı Soyadı
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