Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

Table 3

Sixth-order approximate numerical solution of equation (25) at different values of the fractional order α and the absolute error E = |u_exact − u_α = 1 | for u (x, y, z, t) by FRDTM.

x	y	z	t	FRDTM for different values of α				uexact	Error (E)
				0.6	0.65	0.6	0.5			−287.047	−15.1344	2.09635	2.63837	2.63837	0
1	−2317.74	−321.166	−16.9664				1.6243	1.62437	7E − 05
0.8	0.5	2.33312	2.50559			2.6387	2.69322	2.69322	0
	1	1.65806	1.65806			1.65806	1.65806	1.65814	8E − 05
0.7	0.75	0.6	0.5	2.3115	2.48237	2.61425	2.66827	2.66827	0
			1	1.6427	1.6427	1.6427	1.6427	1.64278	8E − 05
		0.8	0.5	2.29114	2.46051	2.59122	2.64476	2.64476	0
			1	1.62823	1.62823	1.62823	1.62823	1.6283	7E − 05
0.8	0.85	0.6	0.5	2.36272	2.53738	2.67217	2.72739	2.72739	0
			1	1.6791	1.6791	1.6791	1.6791	1.67917	7E − 05
		0.8	0.5	2.28352	2.45233	2.58261	2.63597	2.63597	0
			1	1.62282	1.62282	1.62282	1.62282	1.62289	7E − 05
0.9	0.9	0.6	0.5	2.40744	2.5854	2.72275	2.77901	2.77901	0
			1	1.71088	1.71088	1.71088	1.71088	1.71096	8E − 05
		0.8	0.5	2.29129	2.46067	2.59139	2.64494	2.64494	0
			1	1.62834	1.62834	1.62834	1.62834	1.62841	7E − 05