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 | 5.4687e−03 | 1.3728e−02 | |
1/20 | 1.2413e−03 | 2.1393 | 2.2152e−02 | |||
1/40 | 2.9794e−04 | 2.0588 | 4.9608e−02 | |||
1/80 | 7.3348e−05 | 2.0222 | 1.9594e−01 | |||
1.4 | −0.093 | −0.09 | 1/10 | 1.4523e−03 | 1.3728e−02 | |
1/20 | 2.8548e−04 | 2.3468 | 2.2776e−02 | |||
1/40 | 6.7785e−05 | 2.0744 | 4.8048e−02 | |||
1/80 | 1.6770e−05 | 2.0151 | 1.8876e−01 | |||
1.6 | −0.1 | −0.062 | 1/10 | 3.3311e−03 | 1.3104e−02 | |
1/20 | 7.7293e−04 | 2.1076 | 1.9968e−02 | |||
1/40 | 1.8976e−04 | 2.0262 | 4.5240e−02 | |||
1/80 | 4.7234e−05 | 2.0063 | 1.9656e−01 | |||
1.8 | −0.055 | −0.009 | 1/10 | 7.5583e−03 | 1.4976e−02 | |
1/20 | 1.8800e−03 | 2.0073 | 2.0904e−02 | |||
1/40 | 4.6938e−04 | 2.0019 | 4.8048e−02 | |||
1/80 | 1.1730e−04 | 2.0006 | 1.8970e−01 |