Research Article
Series Solutions of Time-Fractional PDEs by Homotopy Analysis Method
Table 2
Approximate
solution of (
4.14) for some values of
using the 4-term HAM approximation,
,
with
and
| | | | | | | | | | | | | | Exact |
| 0.2 | 0.25 | 0.060049 | 0.060199 | 0.048780 | 0.048788 | 0.043403 | 0.043404 | 0.043403 | 0.50 | 0.240195 | 0.240795 | 0.195119 | 0.195152 | 0.173610 | 0.173617 | 0.173611 | 0.75 | 0.540439 | 0.541789 | 0.439018 | 0.439092 | 0.390623 | 0.390638 | 0.390625 | 1.0 | 0.960781 | 0.963180 | 0.780477 | 0.780607 | 0.694441 | 0.694468 | 0.694444 |
| 0.4 | 0.25 | 0.074536 | 0.076976 | 0.045434 | 0.045821 | 0.031853 | 0.031904 | 0.031888 | 0.50 | 0.298142 | 0.307903 | 0.181736 | 0.183285 | 0.127412 | 0.127616 | 0.127551 | 0.75 | 0.670821 | 0.692783 | 0.408907 | 0.412392 | 0.286677 | 0.287137 | 0.286990 | 1.0 | 1.192570 | 1.231614 | 0.726946 | 0.733141 | 0.509649 | 0.510465 | 0.510204 |
| 0.6 | 0.25 | 0.091469 | 0.099717 | 0.045907 | 0.048048 | 0.023920 | 0.024414 | 0.024414 | 0.50 | 0.365878 | 0.398867 | 0.183626 | 0.192191 | 0.095680 | 0.097656 | 0.097656 | 0.75 | 0.823225 | 0.897450 | 0.413159 | 0.432430 | 0.215280 | 0.219727 | 0.219727 | 1.0 | 1.463511 | 1.595467 | 0.734504 | 0.768765 | 0.382720 | 0.390626 | 0.390625 |
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