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where we have neglected higher order terms because
It is seen
that the relative error defined as
is given by
and
are used to approximate
and
respectively, we have
The relative error is quantified by The preceding analysis shows
that the use of more forward steps does not warrant an improvement
in the accuracy. In fact the accuracy is reduced if more forward steps
are employed. Also observed is that the relative error is linearly
proportional to the step size
3.2 Two-Step Algorithm
To improve the accuracy, a two-step algorithm similar to that using
numerical Laplace inversion for switched linear circuits was proposed in
[48]. In this approach, a forward step from to is taken first.
It is then followed by a backward step of the same step size. Re-writing
(5.22) with step size
gives
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