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 | 4.6812e−03 | 1.2119e−02 | |
1/20 | 1.1156e−03 | 2.0691 | 2.1528e−02 | |||
1/40 | 2.6920e−04 | 2.0511 | 4.9296e−02 | |||
1/80 | 6.6095e−05 | 2.0261 | 1.8533e−01 | |||
1.4 | −0.093 | −0.09 | 1/10 | 3.5917e−03 | 1.1856e−02 | |
1/20 | 8.0067e−04 | 2.1654 | 1.9344e−02 | |||
1/40 | 1.8738e−04 | 2.0952 | 5.0544e−02 | |||
1/80 | 4.5523e−05 | 2.0413 | 1.9469e−01 | |||
1.6 | −0.1 | −0.062 | 1/10 | 2.8683e−03 | 1.5912e−02 | |
1/20 | 6.8778e−04 | 2.0602 | 1.7784e−02 | |||
1/40 | 1.7060e−04 | 2.0113 | 4.4928e−02 | |||
1/80 | 4.2575e−05 | 2.0025 | 1.8221e−01 | |||
1.8 | −0.055 | −0.009 | 1/10 | 4.2551e−03 | 1.3104e−02 | |
1/20 | 1.0522e−03 | 2.0158 | 1.8408e−02 | |||
1/40 | 2.6237e−04 | 2.0037 | 4.4304e−02 | |||
1/80 | 6.5551e−05 | 2.0009 | 1.9531e−01 |