Theory and Modern Applications
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 | 1.3356e−03 | 1.5912e−02 | |
1/20 | 3.5152e−04 | 1.9258 | 2.2152e−02 | |||
1/40 | 9.0044e−05 | 1.9649 | 4.8672e−02 | |||
1/80 | 2.2629e−05 | 1.9925 | 1.9594e−01 | |||
1.4 | −0.093 | −0.09 | 1/10 | 1.4612e−03 | 1.3728e−02 | |
1/20 | 4.2047e−04 | 1.7971 | 1.9344e−02 | |||
1/40 | 1.0892e−04 | 1.9487 | 5.0856e−02 | |||
1/80 | 2.7456e−05 | 1.9881 | 2.0280e−01 | |||
1.6 | −0.1 | −0.062 | 1/10 | 2.2694e−03 | 1.2480e−02 | |
1/20 | 5.0328e−04 | 2.1729 | 1.9656e−02 | |||
1/40 | 1.2209e−04 | 2.0434 | 5.0544e−02 | |||
1/80 | 3.0302e−05 | 2.0105 | 1.9313e−01 | |||
1.8 | −0.055 | −0.009 | 1/10 | 7.1897e−03 | 1.4664e−02 | |
1/20 | 1.7878e−03 | 2.0077 | 2.2464e−02 | |||
1/40 | 4.4632e−04 | 2.0020 | 5.1480e−02 | |||
1/80 | 1.1154e−04 | 2.0005 | 2.0062e−01 |