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

Table 3

The HAM results for 𝐸(𝑥,𝑡) for the 8th-order approximate in comparison with the analytical solution with initial conditions (3.11) when ℏ=−1,𝑘=0.05,𝑘₁=1,𝑠=0.33,𝛽=1.

𝑡𝑖
𝑥𝑖	0.1	0.2	0.3	0.4	0.5
0.1	5.1079×10^−15	1.008416×10^−13	5.6412×10^−13	1.779969×10^−12	4.42412×10^−12
0.2	1.517338×10^−22	6.7515×10^−13	4.35941×10^−12	1.527263×10^−12	3.9370×10^−12
0.3	5.167×10^−15	3.3395×10^−14	3.2705×10^−13	1.27024×10^−12	3.4467×10^−12
0.4	1.027×10^−14	6.0992×10^−21	2.1885×10^−13	1.02169×10^−12	.9686×10^−12
0.5	1.525×10^−14	3.3136×10^−14	1.08417×10^−13	7.6228×10^−13	2.4632×10^−12