Theory and Modern Applications
Table 8 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 | CN-TWSGD | ||
|---|---|---|---|---|---|---|
\(\|e\|_{L_{2}}\) | Order | CPU time | ||||
1.2 | −0.042 | −0.065 | 1/10 | 4.5730e−02 | 1.3416e−02 | |
1/20 | 1.1805e−02 | 1.9537 | 1.6536e−02 | |||
1/40 | 2.9742e−03 | 1.9888 | 4.9608e−02 | |||
1/80 | 7.4490e−04 | 1.9974 | 1.9594e−01 | |||
1.4 | −0.093 | −0.09 | 1/10 | 2.8404e−02 | 1.4040e−02 | |
1/20 | 7.1673e−03 | 1.9866 | 1.9032e−02 | |||
1/40 | 1.7961e−03 | 1.9966 | 5.3352e−02 | |||
1/80 | 4.4950e−04 | 1.9985 | 1.8876e−01 | |||
1.6 | −0.1 | −0.062 | 1/10 | 1.7727e−02 | 1.3728e−02 | |
1/20 | 4.3929e−03 | 2.0127 | 1.9032e−02 | |||
1/40 | 1.0962e−03 | 2.0027 | 4.8672e−02 | |||
1/80 | 2.7415e−04 | 1.9995 | 1.9095e−01 | |||
1.8 | −0.055 | −0.009 | 1/10 | 1.5124e−02 | 1.1544e−02 | |
1/20 | 3.7756e−03 | 2.0021 | 2.0280e−02 | |||
1/40 | 9.4332e−04 | 2.0009 | 4.7424e−02 | |||
1/80 | 2.3587e−04 | 1.9998 | 1.8627e−01 | |||