Theory and Modern Applications
Table 9 Errors and corresponding observation orders at \(t=1\), \(\lambda =2\)
From: Second-order numerical methods for the tempered fractional diffusion equations
α | \(\beta _{3}\) | \(\gamma _{3}\) | h = τ | Proposed | ||
|---|---|---|---|---|---|---|
\(\|e\|_{L_{2}}\) | Order | CPU time | ||||
1.2 | −0.042 | −0.065 | 1/10 | 2.9290e−02 | 1.2792e−02 | |
1/20 | 7.2154e−03 | 2.0213 | 1.9656e−02 | |||
1/40 | 1.8028e−03 | 2.0008 | 4.7112e−02 | |||
1/80 | 4.5156e−04 | 1.9972 | 1.8907e−01 | |||
1.4 | −0.093 | −0.09 | 1/10 | 1.4051e−02 | 1.4664e−02 | |
1/20 | 3.3112e−03 | 2.0852 | 1.9344e−02 | |||
1/40 | 8.3063e−04 | 1.9951 | 4.4928e−02 | |||
1/80 | 2.0919e−04 | 1.9894 | 1.8377e−01 | |||
1.6 | −0.1 | −0.062 | 1/10 | 1.6352e−02 | 1.4040e−02 | |
1/20 | 3.8004e−03 | 2.1052 | 2.0280e−02 | |||
1/40 | 9.3219e−04 | 2.0275 | 4.8672e−02 | |||
1/80 | 2.3242e−04 | 2.0039 | 1.8751e−01 | |||
1.8 | −0.055 | −0.009 | 1/10 | 2.3758e−02 | 1.4976e−02 | |
1/20 | 6.0638e−03 | 1.9701 | 1.8720e−02 | |||
1/40 | 1.5231e−03 | 1.9932 | 5.0544e−02 | |||
1/80 | 3.8119e−04 | 1.9984 | 1.9126e−01 | |||