Theory and Modern Applications
From: Second-order numerical methods for the tempered fractional diffusion equations
α | h = τ | λ = 2 | λ = 3 | λ = 5 | |||
---|---|---|---|---|---|---|---|
\(\|e\|_{L_{2}}\) | Order | \(\|e\|_{L_{2}}\) | Order | \(\|e\|_{L_{2}}\) | Order | ||
1.2 | 1/10 | 4.4064e−03 | 7.3432e−03 | 1.3289e−02 | |||
1/20 | 1.4170e−03 | 1.6368 | 2.3874e−03 | 1.6210 | 4.6713e−03 | 1.5083 | |
1/40 | 4.4624e−04 | 1.6669 | 7.1388e−04 | 1.7417 | 1.3593e−03 | 1.7810 | |
1/80 | 1.4351e−04 | 1.6367 | 2.1251e−04 | 1.7482 | 3.7612e−04 | 1.8536 | |
1.5 | 1/10 | 2.7871e−04 | 6.9236e−04 | 2.1027e−03 | |||
1/20 | 9.6202e−05 | 1.5346 | 2.3030e−04 | 1.5880 | 7.2237e−04 | 1.5414 | |
1/40 | 3.1225e−05 | 1.6234 | 7.2323e−05 | 1.6710 | 2.3189e−04 | 1.6393 | |
1/80 | 1.0186e−05 | 1.6161 | 2.1899e−05 | 1.7236 | 6.6164e−05 | 1.8093 | |
1.8 | 1/10 | 2.6714e−04 | 2.7940e−04 | 3.2526e−04 | |||
1/20 | 3.7920e−05 | 2.8166 | 3.7952e−05 | 2.8801 | 3.9166e−05 | 3.0539 | |
1/40 | 5.2055e−06 | 2.8649 | 5.1329e−06 | 2.8863 | 5.0821e−06 | 2.9461 | |
1/80 | 7.0658e−07 | 2.8811 | 6.9299e−07 | 2.8889 | 6.8096e−07 | 2.8998 |