THE Q-HOMOTOPY ANALYSIS METHOD (Q-HAM) - IJAMM
THE Q-HOMOTOPY ANALYSIS METHOD (Q-HAM) - IJAMM
THE Q-HOMOTOPY ANALYSIS METHOD (Q-HAM) - IJAMM
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64<br />
solutions<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
Int. J. of Appl. Math and Mech. 8 (15): 51-75, 2012.<br />
M. A. El-Tawil and S. N. Huseen<br />
0.2 0.2 0.4 0.6 0.8 1.0<br />
Figure : Comparison between of <strong>HAM</strong>(q-<strong>HAM</strong> and q-<strong>HAM</strong>(<br />
with exact solution of (18) with( .<br />
The absolute errors of the 15 th order solutions q-<strong>HAM</strong> approximate using different values of<br />
compared with 15 th order solutions <strong>HAM</strong> approximate are shown in figures (15,16).<br />
These figures show that the series solution obtained by <strong>HAM</strong> is more accurate at<br />
but at larger the series solution obtained by q-<strong>HAM</strong> at converge faster than<br />
(<strong>HAM</strong>).<br />
Absolute Error<br />
0.00005<br />
0.00004<br />
0.00003<br />
0.00002<br />
0.00001<br />
0.1 0.2 0.3 0.4 0.5<br />
Figure : The Absolute error of of q-<strong>HAM</strong> ( for problem (18) at<br />
and using<br />
x<br />
x<br />
Exact<br />
U 15 n 100<br />
U 15 n 1<br />
A.E n 1<br />
A.E n 100
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