Solving Famous Nonlinear Coupled Equations with Parameters Derivative by Homotopy Analysis Method

Table 1

The comparison of the results of the HAM (ℎ=−1) and exact solution for the 𝑢(𝑥,𝑡), 𝛼=𝛽=1.

x	t	𝜙6	u(𝑥,𝑡)	Realtive error
10	0.01	−5.3861e-001	−0.9002497662	4.5253𝑒×10^−13
10	0.02	−5.3325e-001	−0.8912921314	1.4459×10^−11
10	0.03	−5.2794e-001	−0.8824236265	1.0962×10^−10
5	0.01	−0.9493828183	−0.9493828187	7.9781×10^−13
5	0.02	−0.9399363019	−0.9399363019	2.5486×10^−11
5	0.03	−0.9305837792	−0.9305837793	1.9322×10^−10
-2	0.01	−0.5386080102	−0.5386080104	7.5651×10^−13
-2	0.02	−0.5332487712	−0.5332487712	2.4167×10^−11
-2	0.03	−0.5279428571	−0.5279428572	1.8322×10^−10