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Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

Ali Kurt
Ali Kurt
, 
Mehmet Şenol
Mehmet Şenol
, 
Orkun Tasbozan
Orkun Tasbozan
 y 
Mehar Chand
Mehar Chand
   | 24 dic 2019
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Publicado en línea: 24 dic 2019
Páginas: 523 - 534
Recibido: 23 abr 2019
Aceptado: 04 jul 2019
DOI: https://doi.org/10.2478/AMNS.2019.2.00049
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© 2019 Ali Kurt et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 Public License.

Fig. 1

The surface plot of the PIA solution u4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.75.
The surface plot of the PIA solution u4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.75.

Fig. 2

The surface plot of the PIA solution v4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.75.
The surface plot of the PIA solution v4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.75.

Fig. 3

The surface plot of the PIA solution u4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.85.
The surface plot of the PIA solution u4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.85.

Fig. 4

The surface plot of the PIA solution v4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.85.
The surface plot of the PIA solution v4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.85.

Fig. 5

The surface plot of the PIA solution u4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.95.
The surface plot of the PIA solution u4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.95.

Fig. 6

The surface plot of the PIA solution v4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.95.
The surface plot of the PIA solution v4(x, y, t) for ℜ = 100 and t = 0.1 when α = 0.95.

PIA (u4(x, y, t)) and exact solution values with absolute errors for y = 1, t = 0.1 and ℜ = 100.

α = 0.75 α = 0.85 α = 0.95
x PIA Exact Error PIA Exact Error PIA Exact Error
0.0 0.903993 0.903996 2.72276E-6 0.911928 0.911928 4.58229E-7 0.917015 0.917015 8.27357E-8
0.1 0.911369 0.911371 2.60627E-6 0.91883 0.918831 4.36394E-7 0.923600 0.923600 7.85330E-8
0.2 0.918305 0.918308 2.43193E-6 0.925300 0.925301 4.05356E-7 0.929761 0.929761 7.27317E-8
0.3 0.924809 0.924811 2.21778E-6 0.931348 0.931348 3.68115E-7 0.935508 0.935508 6.58693E-8
0.4 0.930889 0.930891 1.97981E-6 0.936986 0.936986 3.27310E-7 0.940856 0.940856 5.84150E-8
0.5 0.936559 0.936561 1.73155E-6 0.94223 0.942230 2.85150E-7 0.945821 0.945821 5.07597E-8
0.6 0.941833 0.9411865 1.48390E-6 0.947095 0.947095 2.43396E-7 0.950421 0.950421 4.32130E-8
0.7 0.946727 0.946729 1.24520E-6 0.951600 0.951600 2.03383E-7 0.954674 0.954674 3.60076E-8
0.8 0.951260 0.951261 1.02143E-6 0.955763 0.955763 1.66055E-7 0.958600 0.958600 2.93064E-8
0.9 0.955449 0.95545 8.16543E-7 0.959603 0.959603 1.32019E-7 0.962216 0.962216 2.32127E-8
1.0 0.959314 0.959314 6.32769E-7 0.963139 0.963139 1.01605E-7 0.965542 0.965542 1.77807E-8

PIA (v4(x, y, t)) and exact solution values with absolute errors for y = 1, t = 0.1 and ℜ = 100.

α = 0.75 α = 0.85 α = 0.95
x PIA Exact Error PIA Exact Error PIA Exact Error
0.0 0.604355 0.604352 2.95952E-6 0.595730 0.595730 4.98075E-7 0.590201 0.590201 8.99301E-8
0.1 0.596338 0.596335 2.83291E-6 0.588228 0.588228 4.74342E-7 0.583043 0.583043 8.53620E-8
0.2 0.588799 0.588796 2.64341E-6 0.581195 0.581195 4.40604E-7 0.576347 0.576347 7.90562E-8
0.3 0.581729 0.581727 2.41063E-6 0.574622 0.574622 4.00125E-7 0.570100 0.570100 7.15971E-8
0.4 0.575120 0.575118 2.15196E-6 0.568493 0.568493 3.55772E-7 0.564287 0.564287 6.34946E-8
0.5 0.568957 0.568956 1.88212E-6 0.562794 0.562794 3.09945E-7 0.558890 0.558890 5.51736E-8
0.6 0.563225 0.563223 1.61293E-6 0.557506 0.557506 2.64561E-7 0.553890 0.553890 4.69707E-8
0.7 0.557905 0.557904 1.35347E-6 0.552609 0.552609 2.21069E-7 0.549267 0.549267 3.91387E-8
0.8 0.552978 0.552977 1.11025E-6 0.548084 0.548084 1.80495E-7 0.545000 0.545000 3.18548E-8
0.9 0.548425 0.548424 8.87547E-7 0.543910 0.543910 1.43499E-7 0.541070 0.541070 2.52312E-8
1.0 0.544224 0.544223 6.87793E-7 0.540066 0.540066 1.10441E-7 0.537454 0.537454 1.93268E-8
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