Research Article
Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
Table 2
Numerical values when
= 0.50, 0.75, and 1.0 for (
61).
| | | | | | FVIM | 2D-FLFs | FVIM | 2D-FLFs | FVIM | 2D-FLFs | Exact |
| 0.25 | 0.25 | 0.12422501 | 0.12225461 | 0.09230374 | 0.09224583 | 0.06250058 | 0.062500 | 0.062500 | 0.50 | 0.24845002 | 0.24450922 | 0.18460748 | 0.18449165 | 0.12500117 | 0.125000 | 0.125000 | 0.75 | 0.37267504 | 0.36676383 | 0.27691122 | 0.27673748 | 0.18750175 | 0.187500 | 0.187500 | 1.00 | 0.49690005 | 0.48901844 | 0.36921496 | 0.36898331 | 0.25000234 | 0.250000 | 0.250000 |
| 0.50 | 0.25 | 0.18377520 | 0.16584130 | 0.15148283 | 0.14985508 | 0.12507592 | 0.125000 | 0.125000 | 0.50 | 0.36755040 | 0.33168259 | 0.30296566 | 0.29971016 | 0.25015184 | 0.250000 | 0.250000 | 0.75 | 0.55132559 | 0.49752389 | 0.45444848 | 0.44956524 | 0.37522776 | 0.375000 | 0.375000 | 1.00 | 0.73510079 | 0.66336518 | 0.60593131 | 0.59942032 | 0.50030368 | 0.500000 | 0.500000 |
| 0.75 | 0.25 | 0.27227270 | 0.20678964 | 0.21407798 | 0.20119503 | 0.18881843 | 0.187500 | 0.187500 | 0.50 | 0.54454540 | 0.41357929 | 0.42815596 | 0.40239005 | 0.37763687 | 0.375000 | 0.375000 | 0.75 | 0.81681810 | 0.62036893 | 0.64223394 | 0.60358508 | 0.56645530 | 0.562500 | 0.562500 | 1.00 | 1.08909080 | 0.82715857 | 0.85631192 | 0.80478011 | 0.75527373 | 0.750000 | 0.750000 |
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