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Information technology of preschool education reform of fine arts based on fractional differential equation


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Fig. 1

Comparison between numerical solutions and exact solutions of the integral equation for m at two different values when m = 1.
Comparison between numerical solutions and exact solutions of the integral equation for m at two different values when m = 1.

Fig. 2

Numerical solutions of the integral equation at different values when m = 16.
Numerical solutions of the integral equation at different values when m = 16.

Fig. 3

Numerical solutions of the integral equation at different values when m = 32.
Numerical solutions of the integral equation at different values when m = 32.

The error results of numerical solution of m under two different values when α, m = 1

m = 16 x values m = 32 x′ values m = 16 numerical solution u¯(si) \overline {\boldsymbol{u}} ({\boldsymbol{s}}_{\boldsymbol{i}}^\prime) m = 32 numerical solution u¯(si) \overline {\boldsymbol{u}} ({\boldsymbol{s}}_{\boldsymbol{i}}^\prime) m = 16 absolute error m = 32 absolute error

0.0312 0.0157 0.8512 0.8458 1.4835E−1 1.2155E−1
0.1563 0.1406 0.8805 0.8782 1.0733E−1 8.7086E −1
0.2813 0.2656 0.8836 0.8847 7.7067E−1 6.3776E −1
0.4063 0.3906 0.8609 0.8651 5.7660E−2 4.9992E −2
0.5313 0.5153 0.8156 0.8224 4.6530E−2 4.1802E −2
0.6562 0.6406 0.7532 0.7617 3.9118E−2 3.3960E −2
0.7814 0.7656 0.6800 0.6895 2.9988E−2 2.1063E −2
0.9062 0.8906 0.6027 0.6124 1.3915E−2 1.4721E −2
Det(A) 4.0422E6 3.2856E13
Cond(A) 11.0262 13.6051
||A−1|| 0.9990 0.9998
em 7.1786E −2 6.2891E −2
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