Solving the Fractional Rosenau-Hyman Equation via Variational Iteration Method and Homotopy Perturbation Method

Table 4

Errors of the approximate solution of fractional Rosenau-Hynam equation using fifth term of HPM and fifth iterate of VIM when 𝛼=1.0 and 𝑐=0.5.

𝑡	𝑥=𝜋/2		𝑥=𝜋		𝑥=3𝜋/2
	VIM	HPM	VIM	HPM	VIM	ADM
0.1	1.0000𝐸−11	2.4346𝐸−09	5.0000𝐸−10	3.4720𝐸−09	2.0000𝐸−10	2.4756𝐸−09
0.2	1.0000𝐸−11	7.7240𝐸−08	5.0000𝐸−10	1.1109𝐸−07	3.0000𝐸−10	7.9858𝐸−08
0.3	1.0000𝐸−11	5.8140𝐸−07	5.0000𝐸−10	8.4330𝐸−07	3.0000𝐸−10	6.1121𝐸−07
0.4	1.0000𝐸−10	2.4280𝐸−06	1.0000𝐸−10	3.5522𝐸−06	9.0000𝐸−10	2.5955𝐸−06
0.5	3.0000𝐸−10	7.3419𝐸−06	4.0000𝐸−10	1.0835𝐸−05	1.9000𝐸−09	7.9805𝐸−06
0.6	1.0000𝐸−09	1.8100𝐸−05	7.0000𝐸−10	2.6942𝐸−05	6.1000𝐸−09	2.0004𝐸−05
0.7	2.6000𝐸−09	3.8743𝐸−05	1.2000𝐸−09	5.8188𝐸−05	1.8300𝐸−08	4.3547𝐸−05
0.8	5.4000𝐸−09	7.4800𝐸−05	2.1000𝐸−09	1.1335𝐸−04	3.9300𝐸−08	8.5496𝐸−05
0.9	1.1110𝐸−07	1.3340𝐸−04	4.0000𝐸−09	2.0405𝐸−04	8.2200𝐸−08	1.5512𝐸−04
1.0	2.1110𝐸−07	2.2370𝐸−04	8.6000𝐸−09	3.4516𝐸−04	1.5230𝐸−07	2.6444𝐸−04