Example: 3D Range Enclosure The Task Let Enclose the range of f on the interval ×   . The Solution 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. This is to load intpakX: > restart; > libname:="/usr/maple/intpakX/lib", libname; > with(intpakX); And this is the solution: > 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]` >

intpakX     Wiss. Rechnen / Softwaretechnologie     FB Mathematik     Bergische Universität Wuppertal