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

Table 3

(a) Comparison of absolute errors of 1st order OHAM solution and 1st order VIM solution for Example 3 at 𝑥=−2.5 and various values of t. (b) Comparison of absolute errors of 1st order OHAM solution and 1st order VIM solution for Example 3 at 𝑥=0 and various values of t. (c) Comparison of absolute errors of 1st order OHAM solution and 1st order VIM solution for Example 3 at 𝑥=−2.5 and various values of t. (d) Comparison of absolute errors of 1st order OHAM solution and 1st order VIM solution for Example 3 at 𝑥=−2.5 and various values of t.

(a)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.687297	0.687094	1.510466×10^−3	2.02246×10^−4
0.04	0.682171	0.68177	3.017151×10^−3	4.0071×10^−4
0.06	0.677041	0.676445	4.521014×10^−3	5.96353×10^−4
0.08	0.671911	0.67112	6.023003×10^−3	7.90121×10^−4
0.10	0.666779	0.665796	7.524051×10^−3	9.82948×10^−4

(b)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.999956	0.997993	2.455556×10^−3	1.96248×10^−3
0.04	0.999822	0.995986	4.822243×10^−3	3.83608×10^−3
0.06	0.9996	0.993979	7.100106×10^−3	5.62086×10^−3
0.08	0.999289	0.991972	9.289225×10^−3	7.3169×10^−3
0.10	0.99889	0.989965	1.138971×10^−3	8.92431×10^−3

(c)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.697537	0.697529	1.247750×10^−3	7.71606×10^−6
0.04	0.702649	0.702639	2.501243×10^−3	9.6889×10^−6
0.06	0.707754	0.707749	3.761480×10^−3	4.91862×10^−6
0.08	0.712851	0.712859	5.029472×10^−3	7.60727×10^−6
0.10	0.71794	0.717969	6.306245×10^−3	2.89136×10^−5

(d)  

𝑡	Exact solution	OHAM solution	Absolute error VIM	Absolute error OHAM
0.02	0.283601	0.283512	6.719964×10^−4	889401×10^−5
0.04	0.286816	0.286609	1.315023×10^−3	20685×10^−4
0.06	0.29006	0.289706	1.928998×10^−3	353812×10^−4
0.08	0.293333	0.292803	2.513842×10^−3	529904×10^−4
0.10	0.296636	0.295901	3.069485×10^−3	735198×10^−4