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Theory and Modern Applications

Table 2 The numerical convergence orders in spatial direction with \(\pmb{\tau=\frac{1}{10{,}000}}\)

From: A second order box-type scheme for fractional sub-diffusion equation with spatially variable coefficient under Neumann boundary conditions

h

α  = 0.2

α  = 0.5

α  = 0.8

\(\boldsymbol{E_{\infty}(h,\tau)}\)

Order( h )

\(\boldsymbol{E_{\infty}(h,\tau)}\)

Order( h )

\(\boldsymbol{E_{\infty}(h,\tau)}\)

Order( h )

1/8

1.6761e−002

*

1.1880e−002

*

8.3067e−003

*

1/16

4.1978e−003

1.9974

2.9752e−003

1.9975

2.0799e−003

1.9978

1/32

1.0499e−003

1.9994

7.4416e−004

1.9993

5.2021e−004

1.9993

1/64

2.6253e−004

1.9997

1.8609e−004

1.9996

1.3010e−004

1.9995