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

Table 3

Errors of the approximate solution of fractional Rosenau-Hynam equation using 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	HPM
0.1	1.0000𝐸−11	1.0000𝐸−11	5.0000𝐸−10	1.0000𝐸−11	2.0000𝐸−10	1.0000𝐸−11
0.2	1.0000𝐸−11	1.2173𝐸−09	5.0000𝐸−10	1.7360𝐸−09	3.0000𝐸−10	1.2378𝐸−09
0.3	1.0000𝐸−11	9.2044𝐸−09	5.0000𝐸−10	1.3182𝐸−08	3.0000𝐸−10	9.4375𝐸−09
0.4	1.0000𝐸−10	3.8620𝐸−08	1.0000𝐸−10	5.5542𝐸−08	9.0000𝐸−10	3.9929𝐸−08
0.5	3.0000𝐸−10	1.1734𝐸−07	4.0000𝐸−10	1.6948𝐸−07	1.9000𝐸−09	1.2233𝐸−07
0.6	1.0000𝐸−09	2.9070𝐸−07	7.0000𝐸−10	4.2165𝐸−07	6.1000𝐸−09	3.0561𝐸−07
0.7	2.6000𝐸−09	6.2550𝐸−07	1.2000𝐸−09	9.1117𝐸−07	1.8300𝐸−08	6.6309𝐸−07
0.8	5.4000𝐸−09	1.2140𝐸−06	2.1000𝐸−09	1.7761𝐸−06	3.9300𝐸−08	1.2978𝐸−06
0.9	1.1110𝐸−07	2.1777𝐸−06	4.0000𝐸−09	3.1998𝐸−06	8.2200𝐸−08	2.3474𝐸−06
1.0	2.1110𝐸−07	3.6709𝐸−06	8.6000𝐸−09	5.4173𝐸−06	1.5230𝐸−07	3.9903𝐸−06