Example: 2D Range Enclosure     		  
 
 
 
 
  The Task


Let

Enclose the range of f on the interval [0.5,2].

 
 
 
 
 
  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:

  
 

> X:=[0.5,2.];

X := [.5, 2.]

> f:=x->exp(-x^2)*sin(Pi*x^3);

f := proc (x) options operator, arrow; exp(-x^2)*si...

> compute_range(f,X,3); 

Start range enclosure =   [-.7788007834, .7788007834]

Range_enclosure after step 3 =  [-.3233867682,.6639743998]

[Maple Plot]

> compute_range(f,X,6); 

Start range enclosure =   [-.7788007834, .7788007834]

Range_enclosure after step 6 =  [-.2834388814,.5563221619]

[Maple Plot]

> compute_range(f,X,9); 

Start range enclosure =   [-.7788007834, .7788007834]

Range_enclosure after step 9 =  [-.274568686 ,.5530593853]

[Maple Plot]

>

 
 
 
 
 

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