# Suppose we have at mesh points a = t0 (a) By repeating the calculation using the same method at the.

Suppose we
have at mesh points a = t0 < t1="">< ···="">< tn_1="">< tn="b" the="" result="" of="" a="" calculation="" of="" a="" solution="" for="" a="" given="" smooth="" initial="" value="" ode="" using="" a="" one-step="" method="" of="" order="" q.="">

(a) By
repeating the calculation using the same method at the mesh points t0, t0+t1 2
,t1, t1+t2 2 , t2,…tN_1, tN_1+tN 2 ,tN , i.e., with each of the
original step sizes hi = ti+1 _ ti halved, show how an estimate for the
global error may be obtained.

(b) Estimate
global errors for the results of Example 16.7
»

Suppose we
have at mesh points a = t0 < t1="">< ···="">< tn_1="">< tn="b" the="" result="" of="" a="" calculation="" of="" a="" solution="" for="" a="" given="" smooth="" initial="" value="" ode="" using="" a="" one-step="" method="" of="" order="" q.="">

(a) By
repeating the calculation using the same method at the mesh points t0, t0+t1 2
,t1, t1+t2 2 , t2,…tN_1, tN_1+tN 2 ,tN , i.e., with each of the
original step sizes hi = ti+1 _ ti halved, show how an estimate for the
global error may be obtained.

(b) Estimate
global errors for the results of Example 16.7 without using the known exact
solution. Compare your estimates with the exact errors given in Table 16.2.

»

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