Theory and Modern Applications
From: Second-order numerical methods for the tempered fractional diffusion equations
λ | h = τ | \(\gamma _{3}=-0.065\) | \(\gamma _{3}=0\) | \(\gamma _{3}=0.046\) | |||
---|---|---|---|---|---|---|---|
\(\|e\|_{L_{2}}\) | Order | \(\|e\|_{L_{2}}\) | Order | \(\|e\|_{L_{2}}\) | Order | ||
1/50 | 1/10 | 1.3091e−03 | 8.9048e−03 | 1.5872e−02 | |||
1/20 | 3.4456e−04 | 1.9257 | 2.2077e−03 | 2.0120 | 3.9986e−03 | 1.9889 | |
1/40 | 8.8261e−05 | 1.9649 | 5.4891e−04 | 2.0079 | 9.9862e−04 | 2.0015 | |
1/80 | 2.2181e−05 | 1.9925 | 1.3688e−04 | 2.0037 | 2.4933e−04 | 2.0019 | |
0 | 1/10 | 5.4687e−03 | 1.3477e−02 | 1.9237e−02 | |||
1/20 | 1.2413e−03 | 2.1393 | 3.2862e−03 | 2.0360 | 4.7459e−03 | 2.0191 | |
1/40 | 2.9794e−04 | 2.0588 | 8.1182e−04 | 2.0172 | 1.1770e−03 | 2.0116 | |
1/80 | 7.3348e−05 | 2.0222 | 2.0193e−04 | 2.0073 | 2.9313e−04 | 2.0055 | |
2 | 1/10 | 3.9639e−03 | 8.1213e−03 | 1.0887e−02 | |||
1/20 | 9.7650e−04 | 2.0212 | 2.1455e−03 | 1.9204 | 2.9861e−03 | 1.8663 | |
1/40 | 2.4398e−04 | 2.0009 | 5.4410e−04 | 1.9794 | 7.6695e−04 | 1.9611 | |
1/80 | 6.1112e−05 | 1.9972 | 1.3648e−04 | 1.9952 | 1.9300e−04 | 1.9905 |