Table 1.

The global error of numerical solutions for the exponential Euler method

Step size	${\mathit{ϵ}}_{\mathbf{2}}$	${\mathit{ϵ}}_{\mathbf{4}}$
$h=\frac{1}{2}$	0.11758788103726	0.05128510485760
$h=\frac{1}{4}$	0.01076456781468	0.00178190502421
$h=\frac{1}{8}$	4.226428624973588e − 004	2.606318250482847e − 004
$h=\frac{1}{16}$	1.080022443102593e − 004	6.629709170569013e − 005
$h=\frac{1}{32}$	1.325175503903862e − 005	1.152618733195335e − 005
$h=\frac{1}{64}$	3.097379961005242e − 007	2.047860964726653e − 006
$h=\frac{1}{128}$	8.055605114301942e − 009	5.371039941796389e − 007