Let

Enclose the range of f on the interval

×   .

Here's the Maple Worksheet solving the task with intpakX. The results for three different numbers of iteration steps are given. The numerical results are stored in a global variable list_of_ranges.

> restart;

> libname:="/usr/maple/intpakX/lib", libname;

> with(intpakX);
 

> T:=[evalf(Pi/8),evalf(Pi/2)];

> S:=[evalf(Pi/8),evalf(Pi/2)];

> g:=(x,y)->exp(-x*y)*sin(Pi*x^2*y^2);

> compute_range3d(g,T,S,4);

Start range enclosure =  [-.8570898115, .8570898115]

Range enclosure after step 1 =  [-.8570898115,.8570898115]

Range enclosure after step 2 =  [-.6800891261,.8570898115]

Range enclosure after step 3 =  [-.6800891261,.8486122905]

Range enclosure after step 4 =  [-.5093193828,.7559256232]

> compute_range3d(g,T,S,6);

Start range enclosure =  [-.8570898115, .8570898115]

Range enclosure after step 1 =  [-.8570898115,.8570898115]

Range enclosure after step 2 =  [-.6800891261,.8570898115]

Range enclosure after step 3 =  [-.6800891261,.8486122905]

Range enclosure after step 4 =  [-.5093193828,.7559256232]

Range enclosure after step 5 =  [-.4602976258,.7134506554]

Range enclosure after step 6 =  [-.3998935848,.6398824698]

> compute_range3d(g,T,S,8);

Start range enclosure =  [-.8570898115, .8570898115]

Range enclosure after step 1 =  [-.8570898115,.8570898115]

Range enclosure after step 2 =  [-.6800891261,.8570898115]

Range enclosure after step 3 =  [-.6800891261,.8486122905]

Range enclosure after step 4 =  [-.5093193828,.7559256232]

Range enclosure after step 5 =  [-.4602976258,.7134506554]

Range enclosure after step 6 =  [-.3998935848,.6398824698]

Range enclosure after step 7 =  [-.3801619988,.6225502393]

Range enclosure after step 8 =  [-.3483950993,.5783521315]

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