Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Publié en ligne: 22 nov. 2021 Pages: 465 - 474 Reçu: 17 juin 2021 Accepté: 24 sept. 2021 © 2021 Zhang et al., published by Sciendo This work is licensed under the Creative Commons Attribution 4.0 International License.
Fig. 1 Relationship between CPU time consumed by DFD and FFD and time step in log-log coordinates Fig. 2 Mass and time evolution diagram of one-dimensional time-fractional Allen-Calm equation Fig. 3 Phase function of two-dimensional time-fractional Allen-Calm equation and change of energy with time L2 error of numerical solutions obtained by DFD and FFD when Δt = 2−16 and α = 0.7 are fixed
FFD
DFD
N
E(h ,Δt )
Cov
CPU (s)
E(h ,Δt )
Cov
CPU (s)
25
3.4024e−04
2.00
6.69
3.4024e−04
2.00
2652.36
26
8.4964e−05
2.01
10.16
8.4964e−05
2.01
2822.55
27
2.1146e−05
2.02
36.31
2.1146e−05
2.02
3140.38
28
5.2182e−06
-
103.89
5.2182e−06
-
3651.16
L2 error and corresponding spatial convergence order of finite difference decomposition at Δt = 2−16
N
α = 0.2 E(h ,Δt ) Cov
α = 0.5 E(h ,Δt ) Cov
α = 0.8 E(h ,Δt ) Cov
25
4.3385e−04 1.98
3.8225e−04 2.00
3.1800e−04 1.99
26
1.1000e−04 1.92
9.5800e−05 1.99
7.9804e−05 1.98
27
2.9043e−05 1.72
2.4189e−05 1.94
2.0254e−05 1.91
28
8.8305e−06
6.3168e−06
5.3865e−06
L2 error and corresponding time convergence order of finite difference decomposition at h = 2−12
M
α = 0.2 E(h ,Δt ) Cov
α = 0.5 E(h ,Δt ) Cov
α = 0.8 E(h ,Δt ) Cov
25
3.4200e−03 0.77
2.0717e−03 1.03
7.8969e−03 1.21
26
2.0022e−03 0.90
1.0116e−03 1.06
3.4059e−03 1.22
27
1.0715e−03 0.90
4.8658e−04 1.06
1.4612e−03 1.23
28
5.5260e−04
2.3374e−04
6.2398e−04