A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

Table 2

The comparison of the exact solutions with the numerical solutions with 𝛾=0.5, 𝑁=40, and 𝑡_𝑓=0.1 for different values of Δ𝑡 and the error norms 𝐿₂ and 𝐿_∞.

𝑥	Δ𝑡=0.01	Δ𝑡=0.001	Δ𝑡=0.0001	Δ𝑡=0.00001	Exact
0.0	0.000000	0.000000	0.000000	0.000000	0.000000
0.1	0.015039	0.013920	0.013929	0.013930	0.013765
0.2	0.026111	0.026325	0.026347	0.026349	0.026183
0.3	0.035392	0.036034	0.036063	0.036065	0.036037
0.4	0.041638	0.042195	0.042229	0.042233	0.042364
0.5	0.043830	0.044306	0.044341	0.044345	0.044544
0.6	0.041638	0.042195	0.042229	0.042233	0.042364
0.7	0.035392	0.036034	0.036063	0.036065	0.036037
0.8	0.026111	0.026325	0.026347	0.026349	0.026183
0.9	0.015039	0.013920	0.013929	0.013930	0.013765
1.0	0.000000	0.000000	0.000000	0.000000	0.000000
𝐿2×10^3	0.836889	0.142246	0.136548	0.136264
𝐿∞×10^3	1.589369	0.238942	0.203235	0.199723