THE Q-HOMOTOPY ANALYSIS METHOD (Q-HAM) - IJAMM

68
Int. J. of Appl. Math and Mech. 8 (15): 51-75, 2012.
M. A. El-Tawil and S. N. Huseen
To find the valid region of ,the -curves given by the 10 th order q-HAM approximation at
different values of are drawn in figures (19 ,20 and 21).This figures show the
interval of where the value of is constant at certain . We choose the
horizontal line parallel to as a valid region which provides us with a simple way
to adjust and control the convergence region.
5 10 14
4 10 14
3 10 14
2 10 14
1 10 14
U 10 , n
0.06 0.04 0.02 0.02 0.04 0.06
Figure : - curves for the HAM (q-HAM; approximation solution of
problem (1) at different values of .
U 10 , n
2000
1500
1000
500
0.06 0.04 0.02 0.02
Figure : - curves for the q-HAM( approximation solution of
problem (1) at different values of .
h
h
U 10 0.1 ,1
U 10 0.6 ,1
U 10 1,1
U 10 2,1
U 10 0.1 ,10
U 10 0.6 ,10
U 10 1,10
U 10 2,10