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

Table 1

(a) Comparison of absolute errors of 3rd order OHAM solution and 3rd order VIM solution for Example 1 at 𝑥=1.2 and various values of t. (b) Comparison of absolute errors of 3rd order OHAM solution and 3rd order VIM solution for Example 1 at 𝑥=1.4 and various values of t. (c) Comparison of absolute errors of 3rd order OHAM solution and 3rd order VIM solution for Example 1 at 𝑥=1.6 and various values of t.

(a)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.313486	0.313486	1.92728×10^−5	3.146×10^−7
0.04	0.32628	0.32627	3.39912×10^−5	1.01891×10^−5
0.06	0.339596	0.339571	1.301192×10^−4	2.46667×10^−5
0.08	0.353455	0.353416	2.401071×10^−4	3.87876×10^−5
0.10	0.367879	0.367829	3.356920×10^−4	5.08783×10^−5

(b)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.256661	0.256661	1.331×10^−7	3.29357×10^−8
0.04	0.267135	0.267135	2.11230×10^−5	5.45591×10^−7
0.06	0.278037	0.278037	4.57127×10^−5	1.19768×10^−7
0.08	0.289384	0.289387	5.71818×10^−5	2.34162×10^−6
0.10	0.301194	0.301199	3.93977×10^−5	4.79793×10^−6

(c)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.210136	0.210136	1.4946×10^−6	4.27298×10^−7
0.04	0.218712	0.218712	7.2701×10^−6	1.00227×10^−7
0.06	0.227638	0.227635	7.6219×10^−6	2.32488×10^−6
0.08	0.236928	0.23692	6.6969×10^−6	7.99082×10^−6
0.10	0.246597	0.246577	4.44429×10^−5	1.99024×10^−5