Theory and Modern Applications
From: Second-order numerical methods for the tempered fractional diffusion equations
α | \(\beta _{3}\) | \(\gamma _{3}\) | h = τ | CN-TWSGD | ||
---|---|---|---|---|---|---|
\(\|e\|_{L_{2}}\) | Order | CPU time | ||||
1.2 | −0.042 | −0.065 | 1/10 | 1.1101e−02 | 1.2168e−02 | |
1/20 | 2.5816e−03 | 2.1044 | 1.8096e−02 | |||
1/40 | 6.0446e−04 | 2.0945 | 4.2744e−02 | |||
1/80 | 1.4554e−04 | 2.0542 | 1.8408e−01 | |||
1.4 | −0.093 | −0.09 | 1/10 | 6.5309e−03 | 1.3104e−02 | |
1/20 | 1.4729e−03 | 2.1486 | 1.7784e−02 | |||
1/40 | 3.4402e−04 | 2.0981 | 5.3040e−02 | |||
1/80 | 8.3284e−05 | 2.0464 | 4.2120e−01 | |||
1.6 | −0.1 | −0.062 | 1/10 | 3.9390e−03 | 1.2168e−02 | |
1/20 | 9.5249e−04 | 2.0481 | 1.9344e−02 | |||
1/40 | 2.3672e−04 | 2.0085 | 4.6176e−02 | |||
1/80 | 5.9105e−05 | 2.0018 | 1.8627e−01 | |||
1.8 | −0.055 | −0.009 | 1/10 | 4.6667e−03 | 1.1856e−02 | |
1/20 | 1.1555e−03 | 2.0139 | 2.0592e−02 | |||
1/40 | 2.8821e−04 | 2.0033 | 4.2432e−02 | |||
1/80 | 7.2014e−05 | 2.0008 | 1.9375e−01 |