Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation
Publié en ligne: 24 déc. 2019
Pages: 523 - 534
Reçu: 23 avr. 2019
Accepté: 04 juil. 2019
© 2019 Ali Kurt et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 Public License.
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 |