Theory and Modern Applications
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 | 2.3834E-2 | 1.1803E-2 | 5.8392E-3 | 2.9060E-3 | 1.4470E-3 |
1.014 | 1.015 | 1.007 | 1.006 | – | ||
uniform | 5.2830E-2 | 4.2487E-2 | 3.7610E-2 | 3.4421E-2 | 3.1746E-2 | |
0.314 | 0.176 | 0.128 | 0.117 | – | ||
0.4 | adapted | 2.5111E-2 | 1.2307E-2 | 6.0822E-3 | 3.0210E-3 | 1.5042E-3 |
1.029 | 1.017 | 1.010 | 1.006 | – | ||
uniform | 5.3781E-2 | 3.8291E-2 | 3.0463E-2 | 2.5531E-2 | 2.1827E-2 | |
0.490 | 0.330 | 0.255 | 0.226 | – | ||
0.6 | adapted | 2.7214E-2 | 1.3251E-2 | 6.5106E-3 | 3.2190E-3 | 1.5983E-3 |
1.038 | 1.025 | 1.016 | 1.010 | – | ||
uniform | 4.6346E-2 | 2.8593E-2 | 1.9703E-2 | 1.4776E-2 | 1.1579E-2 | |
0.697 | 0.537 | 0.415 | 0.352 | – | ||
0.8 | adapted | 2.9851E-2 | 1.4546E-2 | 7.1417E-3 | 3.5184E-3 | 1.7431E-3 |
1.037 | 1.026 | 1.021 | 1.013 | – | ||
uniform | 3.8350E-2 | 2.1702E-2 | 1.2715E-2 | 8.1152E-3 | 5.5935E-3 | |
0.821 | 0.771 | 0.648 | 0.537 | – |