Theory and Modern Applications
From: Second-order numerical methods for the tempered fractional diffusion equations
λ | h = τ | \(\gamma _{3}=-0.142\) | \(\gamma _{3}=0\) | \(\gamma _{3}=0.333\) | |||
---|---|---|---|---|---|---|---|
\(\|e\|_{L_{2}}\) | Order | \(\|e\|_{L_{2}}\) | Order | \(\|e\|_{L_{2}}\) | Order | ||
1/50 | 1/10 | 7.7227e−03 | 1.0465e−02 | 5.3286e−02 | |||
1/20 | 2.0245e−03 | 1.9315 | 2.6046e−03 | 2.0064 | 1.3526e−02 | 1.9780 | |
1/40 | 5.1203e−04 | 1.9833 | 6.4995e−04 | 2.0027 | 3.3823e−03 | 1.9997 | |
1/80 | 1.2836e−04 | 1.9960 | 1.6239e−04 | 2.0009 | 8.4480e−04 | 2.0013 | |
0 | 1/10 | 5.7263e−03 | 1.1908e−02 | 5.3855e−02 | |||
1/20 | 1.5271e−03 | 1.9068 | 2.9592e−03 | 2.0087 | 1.3568e−02 | 1.9889 | |
1/40 | 3.8755e−04 | 1.9783 | 7.3811e−04 | 2.0033 | 3.3854e−03 | 2.0028 | |
1/80 | 9.7221e−05 | 1.9950 | 1.8439e−04 | 2.0011 | 8.4508e−04 | 2.0022 | |
2 | 1/10 | 2.5444e−03 | 6.6079e−03 | 2.2144e−02 | |||
1/20 | 7.8955e−04 | 1.6882 | 1.7420e−03 | 1.9234 | 6.9946e−03 | 1.6626 | |
1/40 | 2.0774e−04 | 1.9263 | 4.4145e−04 | 1.9804 | 1.8798e−03 | 1.8956 | |
1/80 | 5.2509e−05 | 1.9841 | 1.1072e−04 | 1.9953 | 4.7865e−04 | 1.9735 |