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

Table 2

(a) Absolute error of the solution of Example 2 by optimal homotopy asymptotic method (OHAM) at 𝑥=15, 𝑥=20, and 𝑥=25 and various values of 𝑡. (b) Absolute error of the solution of Example 2 by optimal homotopy asymptotic method (OHAM) at various values of 𝑥 and 𝑡.

(a)  

𝑡	𝑥=15	𝑥=20	𝑥=25
0.01	2.7905×10^−6	2.30504×10^−7	1.89307×10^−8
0.02	2.83577×10^−6	2.35074×10^−7	1.93117×10^−8
0.03	8.32571×10^−6	6.87803×10^−7	5.6488×10^−8
0.04	5.60061×10^−6	4.64385×10^−7	3.81506×10^−8
0.05	1.37955×10^−5	1.13979×10^−6	9.36098×10^−8

(b)  

𝑥	𝑡=0.1	𝑡=0.2	𝑡=0.3	𝑡=0.4	𝑡=0.5
15	2.24995×10^−5	4.36594×10^−5	6.27619×10^−5	9.29866×10^−5	9.16758×10^−5
16	1.36916×10^−5	26576×10^−5	3.82161×10^−5	5.66063×10^−5	5.58636×10^−5
17	8.32101×10^−6	1.61544×10^−5	2.32343×10^−5	3.441×10^−5	3.39789×10^−5
18	5.05308×10^−6	9.81109×10^−6	1.41127×10^−5	2.0899×10^−5	2.06447×10^−5
19	3.0671×10^−6	5.95551×10^−6	8.56725×10^−6	1.26863×10^−5	1.25347×10^−5
20	1.86112×10^−6	3.61396×10^−6	5.19906×10^−6	7.69844×10^−6	7.60747×10^−6
21	1.12913×10^−6	2.19263×10^−6	3.1544×10^−6	4.67075×10^−6	4.61593×10^−6
22	6.84967×10^−7	1.33013×10^−6	1.91361×10^−6	2.83347×10^−6	2.80036×10^−6
23	4.15495×10^−7	8.06854×10^−7	1.1608×10^−6	1.71878×10^−6	1.69874×10^−6
24	2.52026×10^−7	4.89414×10^−7	7.04113×10^−7	1.04256×10^−6	1.03043×10^−6
25	1.52867×10^−7	2.96856×10^−7	4.27085×10^−7	6.32372×10^−7	6.25018×10^−7