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Theory and Modern Applications

Table 2 Error estimates and convergence rates for Example 5.2

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