The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov Equations

Table 4

The HPM results for 𝑛(𝑥,𝑡) for the first three approximations in comparison with the analytical solution with initial conditions (3.11) when 𝑘=0.05,𝑘₁=1,𝑠=0.33,𝛽=1.

𝑡𝑖
𝑥𝑖	0.1	0.2	0.3	0.4	0.5
0.1	4.95717×10^−6	3.71741×10^−6	2.47462×10^−6	1.22975×10^−6	1.62464×10^−8
0.2	2.19054×10^−5	1.95081×10^−5	1.70953×10^−5	1.4669×10^−5	1.22309×10^−5
0.3	4.9547×10^−5	4.61578×10^−5	4.27335×10^−5	3.92765×10^−5	3.57893×10^−5
0.4	8.58804×10^−5	8.17233×10^−5	77.507×10^−5	7.3241×10^−5	6.89074×10^−5
0.5	1.28493×10^−4	1.23818×10^−4	1.1906×10^−4	1.14219×10^−4	1.09299×10^−4