Theory and Modern Applications
From: Second-order numerical methods for the tempered fractional diffusion equations
α | h = τ | λ = 1/50 | λ = 0 | λ = 2 | |||
---|---|---|---|---|---|---|---|
\(\|e\|_{L_{2}}\) | Order | \(\|e\|_{L_{2}}\) | Order | \(\|e\|_{L_{2}}\) | Order | ||
1.2 | 1/10 | 3.6036e−04 | 3.9643e−04 | 3.8557e−04 | |||
1/20 | 9.3836e−05 | 1.9412 | 9.8756e−05 | 2.0051 | 1.0825e−04 | 1.8326 | |
1/40 | 2.4100e−05 | 1.9611 | 2.4944e−05 | 1.9852 | 2.7754e−05 | 1.9636 | |
1/80 | 6.1263e−06 | 1.9759 | 6.2947e−06 | 1.9865 | 6.9556e−06 | 1.9964 | |
1.5 | 1/10 | 4.8058e−04 | 4.9188e−04 | 2.3030e−04 | |||
1/20 | 1.2712e−04 | 1.9186 | 1.2939e−04 | 1.9266 | 6.1371e−05 | 1.9079 | |
1/40 | 3.2771e−05 | 1.9557 | 3.3285e−05 | 1.9588 | 1.5816e−05 | 1.9562 | |
1/80 | 8.3331e−06 | 1.9755 | 8.4560e−06 | 1.9768 | 4.0057e−06 | 1.9813 | |
1.8 | 1/10 | 5.0678e−04 | 5.1402e−04 | 1.7371e−04 | |||
1/20 | 1.3156e−04 | 1.9456 | 1.3326e−04 | 1.9476 | 4.5103e−05 | 1.9454 | |
1/40 | 3.3388e−05 | 1.9783 | 3.3800e−05 | 1.9791 | 1.1761e−05 | 1.9392 | |
1/80 | 8.4106e−06 | 1.9890 | 8.5114e−06 | 1.9896 | 3.0136e−06 | 1.9645 |