Environmental Engineering Reference
In-Depth Information
The solutions of (5.32) are given by
Because
It is seen that the relative error of the two-step algorithm is given
by which is proportional to Since usually the two-step
algorithm with one step forward and one equal step backward provides
better accuracy as compared with the preceding algorithm with two
equal forward steps.
3.3 Four-Step Algorithm
To investigate whether the use of more steps can lead to an improve-
ment in accuracy, a four-step approach in which two forward steps of
equal step size are taken first, followed by two backward steps of the
equal step size, is examined in this section. Using (5.23) as the initial
conditions of the first backward step, we have
The responses of (5.35) are given by
Search WWH ::
Custom Search