Theory and Modern Applications
Table 1 Error estimates and convergence rates for Example 5.1
From: An adaptive moving mesh method for a time-fractional Black–Scholes equation
α | mesh | Number of mesh points N = K | ||||
|---|---|---|---|---|---|---|
64 | 128 | 256 | 512 | 1024 | ||
0.2 | adapted | 4.2452E-3 | 1.5506E-3 | 6.4332E-4 | 2.6089E-4 | 1.0631E-4 |
1.453 | 1.269 | 1.302 | 1.295 | – | ||
uniform | 6.2643E-2 | 5.4541E-2 | 4.7512E-2 | 4.1391E-2 | 3.6056E-2 | |
0.200 | 0.199 | 0.199 | 0.199 | – | ||
0.4 | adapted | 1.4939E-3 | 4.1038E-4 | 1.2679E-4 | 4.2684E-5 | 1.4316E-5 |
1.864 | 1.695 | 1.571 | 1.576 | – | ||
uniform | 3.9175E-2 | 2.9693E-2 | 2.2512E-2 | 1.7067E-2 | 1.2938E-2 | |
0.400 | 0.399 | 0.399 | 0.400 | – | ||
0.6 | adapted | 1.8122E-3 | 6.6974E-4 | 2.5097E-4 | 9.4729E-5 | 3.5860E-5 |
1.436 | 1.416 | 1.406 | 1.401 | – | ||
uniform | 1.7082E-2 | 1.1268E-2 | 7.4347E-3 | 4.9058E-3 3.2370E-3 | ||
0.600 | 0.600 | 0.600 | 0.600 | – | ||
0.8 | adapted | 2.5894E-3 | 1.0941E-3 | 4.6645E-4 | 2.0025E-4 | 8.6448E-5 |
1.243 | 1.230 | 1.220 | 1.212 | – | ||
uniform | 5.8127E-3 | 3.3318E-3 | 1.9131E-3 | 1.0989E-3 | 6.3119E-4 | |
0.803 | 0.800 | 0.800 | 0.800 | – | ||