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Numerical Solutions with Linearization Techniques of the Fractional Harry Dym Equation

Asıf Yokuş

Asıf Yokuş

Department of Actuary, Firat UniversityElazig, Turkey
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Yokuş, Asıf
 et 
Sema Gülbahar

Sema Gülbahar

Department of Mathematics, Harran UniversitySanliurfa, Turkey
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Gülbahar, Sema
  
27 mars 2019
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Publié en ligne: 27 mars 2019
Pages: 35 - 42
Reçu: 14 janv. 2019
Accepté: 21 févr. 2019
DOI: https://doi.org/10.2478/AMNS.2019.1.00004
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© 2019 Asıf Yokuş and Sema Gülbahar, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Comparison of the exact and approximate solution for linearization 2 at h = 0.01
Comparison of the exact and approximate solution for linearization 2 at h = 0.01

Fig. 2

Comparison of the exact and approximate solution for linearization 3 at h=0.01
Comparison of the exact and approximate solution for linearization 3 at h=0.01

Fig. 3

Comparison of the exact and approximate solution for linearization 1, linearization 2, and linearization 3 at h = 0.01
Comparison of the exact and approximate solution for linearization 1, linearization 2, and linearization 3 at h = 0.01

Comparison of the error norms L2 and L∞ that are obtained using the linearization techniques at t = 1,α = 0_9 for different values of Δt, h_

 Lin. I
 Lin. II
 Lin. III
L2 ×102 L∞ ×102 L2 ×102 L∞ ×102 L2 ×102 L∞ ×102
Δt = h = 0.001 0.00002 0.00002 0.00566 0.05664 0.00565 0.05659
Δt = h = 0.05 0.05254 0.08344 0.64556 0.94172 0.58516 0.84499
Δt = h = 0.04 0.02957 0.05128 0.50690 0.82106 0.47224 0.76100
Δt = h = 0.03 0.01418 0.02773 0.36800 0.68391 0.35113 0.65086
Δt = h = 0.02 0.00506 0.01186 0.23124 0.52313 0.22502 0.50855
Δt = h = 0.01 0.00088 0.00285 0.10161 0.32318 0.10046 0.31945
Δt = h = 0.2 2.44568 0.00285 3.12756 3.78842 0.80756 1.29370
Δt = h = 0.1 3.27620 0.41645 1.31211 1.41287 0.94027 0.94563
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Anglais
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Sujets de la revue:
Sciences de la vie, Sciences de la vie, autres, Mathématiques, Mathématiques appliquées, Mathématiques générales, Physique, Physique, autres
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