Figure 1

Asymptotic behavior of the backward Euler approximation with different initial step size${\mathbf{\Delta }}_{\mathbf{0}}$, left:${\mathbf{\Delta }}_{\mathbf{0}}\mathbf{=}\mathbf{0.1}$; right:${\mathbf{\Delta }}_{\mathbf{0}}\mathbf{=}\mathbf{1}$. The left one of Figure 1 describes the mean square asymptotic behavior of the backward Euler approximation $E{|Y_n|}^2$ of Eq. (39) with initial step size ${\mathrm{\Delta }}_0=0.1$; the right one of Figure 1 describes the mean square asymptotic behavior of the backward Euler approximation $E{|Y_n|}^2$ of Eq. (39) with initial step size ${\mathrm{\Delta }}_0=1$.