Optimal Homotopy Asymptotic Method to Nonlinear Damped Generalized Regularized Long-Wave Equation

Table 4

(a) Comparison of absolute errors of 1st order OHAM solution and 1st order VIM solution for Example 4 at 𝑥=0.2 and various values of t. (b) Comparison of absolute errors of 1st order OHAM solution and 1st order VIM solution for Example 4 at 𝑥=0.4 and various values of t. (c) Comparison of absolute errors of 1st order OHAM solution and 1st order VIM solution for Example 4 at 𝑥=0.6 and various values of t. (d) Comparison of absolute errors of 1st order OHAM solution and 1st order VIM solution for Example 4 at 𝑥=1 and various values of t.

(a)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.194735	0.194388	3.596760×10^−4	3.46922×10^−4
0.04	0.190879	0.189563	1.374338×10^−3	1.31649×10^−3
0.06	0.1871	0.184295	2.950802×10^−3	2.8045×10^−3
0.08	0.183395	0.178685	5.000174×10^−3	4.71013×10^−3
0.10	0.179763	0.172828	7.437789×10^−3	6.93584×10^−3

(b)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.381707	0.381449	2.832281×10^−4	2.58242×10^−4
0.04	0.374149	0.373216	1.043581×10^−3	9.32938×10^−4
0.06	0.36674	0.364862	2.151953×10^−3	1.87854×10^−3
0.08	0.359478	0.356523	3.485485×10^−3	2.95526×10^−3
0.10	0.35236	0.348331	4.927456×10^−3	4.02886×10^−3

(c)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.553462	0.55333	1.676249×10^−4	1.31821×10^−4
0.04	0.542503	0.542094	5.651230×10^−4	4.08832×10^−4
0.06	0.53176	0.531101	1.040306×10^−3	6.59364×10^−4
0.08	0.521231	0.520511	1.4483802×10^−3	7.194×10^−4
0.10	0.51091	0.510477	1.651669×10^−3	4.32267×10^−4

(d)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.703151	0.703174	1.439370×10^−4	2.23769×10^−4
0.04	0.689228	0.689438	6.672725×10^−4	2.10203×10^−4
0.06	0.675581	0.676318	1.702709×10^−3	7.37797×10^−4
0.08	0.662203	0.663974	3.376802×10^−3	1.77096×10^−3
0.10	0.649091	0.652558	5.810408×10^−3	3.46734×10^−3