THE SOLUTION OF COUPLED MODIFIED KDV SYSTEM BY THE ...

M. GHOREISHI, A.I.B.MD. ISMAIL, A. RASHID: COUPLED MODIFIED KDV SYSTEM ... 129
nearly parallel to the horizontal axis. From figures 5 and 6, it is clear that the HAM series is
convergent when −1.4 < < −0.6.
Absolute error u forħ⩵0.72 at x⩵15
Absolute error u forħ⩵0.72 at x⩵15
1.10 11 t
4.10 12 t
E5
8.10 12
6.10 12
4.10 12
2.10 12
0
0.0 0.1 0.2 0.3 0.4 0.5
E5
3.10 12
2.10 12
1.10 12
0
0.0 0.1 0.2 0.3 0.4 0.5
Figure 3. The absolute error between HAM solution and the exact solution for = −0.72 at x = 15.
Absolute error u forħ⩵0.72 at x⩵15
2.10 11 t
1.510 11
E5
1.10 11
5.10 12
0
0.0 0.1 0.2 0.3 0.4 0.5
Figure 4. The absolute error between HAM solution and the exact solution for = −0.72 at x = 15.
ħcurve for u t 0,0
20
15
u t 0,0
10
5
0
2.0 1.5 1.0 0.5 0.0 0.5 1.0
ħ
Figure 5. The -curve for u t(0, 0) given by the 5-order HAM approximation solution when H 1(x, t) = 1.