Theory and Modern Applications
Table 1 Solution and residual error for Example 3 when \(\alpha =0.7\) and \(\beta =0.8\) at several values of x and t using 60 terms of the series (\(\hbar =-1\))
From: Homotopy-Sumudu transforms for solving system of fractional partial differential equations
x | t | ||||||
|---|---|---|---|---|---|---|---|
0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 | ||
0 | u | 1. | 1.49505 | 2.01823 | 2.72055 | 3.74817 | 5.42523 |
Eu | 0. | 4.441 10−16 | 4.441 10−16 | 2.220 10−15 | 2.110 10−10 | 2.403 10−6 | |
0.25 | u | 1.28403 | 1.91105 | 2.56371 | 3.42903 | 4.68035 | 6.70162 |
Eu | 1.110 10−16 | 6.661 10−16 | 1.110 10−15 | 6.661 10−16 | 2.522 10−10 | 2.882 10−6 | |
0.5 | u | 1.64872 | 2.4452 | 3.26413 | 4.33873 | 5.87729 | 8.34054 |
Eu | 0. | 0. | 8.882 10−16 | 2.220 10−15 | 3.052 10−10 | 3.495 10−6 | |
0.75 | u | 2.117 | 3.13107 | 4.16348 | 5.50681 | 7.41419 | 10.445 |
Eu | 0. | 6.661 10−16 | 1.332 10−15 | 2.220 10−15 | 3.733 10−10 | 4.282 10−6 | |
1 | u | 2.71828 | 4.01174 | 5.31827 | 7.00666 | 9.38762 | 13.1471 |
Eu | 0. | 2.220 10−16 | 1.332 10−15 | 1.332 10−15 | 4.603 10−10 | 5.293 10−6 | |
0 | v | 1. | 0.77102 | 0.67532 | 0.64818 | 0.69700 | 0.87441 |
Ev | 0 | 8.882 10−16 | 1.110 10−15 | 2.220 10−15 | 8.952 10−11 | 1.013 10−6 | |
0.25 | v | 0.77880 | 0.60431 | 0.53668 | 0.52694 | 0.58472 | 0.76075 |
Ev | 1.110 10−16 | 0 | 6.661 10−16 | 2.2206 10−15 | 8.30 10−11 | 9.413 10−7 | |
0.5 | v | 0.60653 | 0.47448 | 0.42870 | 0.43252 | 0.49728 | 0.67224 |
Ev | 0 | 4.441 10−16 | 2.220 10−16 | 2.220 10−15 | 7.790 10−11 | 8.854 10−7 | |
0.75 | v | 0.47237 | 0.37336 | 0.34461 | 0.35899 | 0.42918 | 0.60330 |
Ev | 0 | 6.661 10−16 | 6.661 10−16 | 2.220 10−15 | 7.403 10−11 | 8.413 10−7 | |
1 | v | 0.36788 | 0.29462 | 0.27912 | 0.30172 | 0.37614 | 0.54961 |
Ev | 0 | 4.441 10−16 | 6.661 10−16 | 1.776 10−15 | 7.097 10−11 | 8.083 10−7 | |