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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 The numerical convergence orders in temporal direction with \(\pmb{h=\frac{1}{3{,}000}}\)

τ	α = 0.2		α = 0.5		α = 0.8
τ	\(\boldsymbol{E_{\infty}(h,\tau)}\)	Order( τ )	\(\boldsymbol{E_{\infty}(h,\tau)}\)	Order( τ )	\(\boldsymbol{E_{\infty}(h,\tau)}\)	Order( τ )
1/4	1.0303e−001	*	1.9759e−001	*	2.0353e−001	*
1/8	2.7328e−002	1.9146	5.2296e−002	1.9177	5.2924e−002	1.9432
1/16	7.0561e−003	1.9534	1.3532e−002	1.9503	1.3588e−002	1.9616
1/32	1.7959e−003	1.9742	3.4573e−003	1.9687	3.4673e−003	1.9704