Concept explainers
In this section we stated that the global truncation errorfor the Euler method applied to an initial value problem over a fixed interval is no more than a constant times the step size
and
Which is the equation of a straight line in the
a) Using the data in Table 8.2.1, calculate the maximum error
b) Plot
c) Do the points in part (b) lie approximately on a singlestraight line? If so, then this is evidence that the assumed expression for
d) Estimate the slope of the line in part (c). If the statementin the text about the magnitude of the global truncation erroris correct, then the slope should be no greater than 1.
Note: Your estimate of the slope p depends on how youchoose the straight line. If you have a curve-fitting routinein your software, you can use it to determine the straight linethat best fits the data. Otherwise, you may wish to resort toless precise methods. For example, you could calculate theslopes of the line segments joining (one or more) pairs ofdata points, and then average your results.
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Differential Equations: An Introduction to Modern Methods and Applications
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