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c18a.c
'
/* ---------------------------------- */
/* save as c18a.c                    */
/* --------------------------------- */
#include  "x_hfile.h"
#include      "fa.h"
/* --------------------------------- */
int main(void)
{
double ay = -1.;
double by =  0;
int    ny = 2*20; 
int    n  = 2*20;
/* --------------------------------- */                 
 clrscrn(); 
 printf(" The Green's theorem :   \n\n");
 
 printf("    (                            (b   (v(x)\n" 
        " int( M(x,y) + dx N(x,y) dy = int( int( (N_x - M_y) dx dy\n"
        "    (c                           (a   (u(x) \n\n\n\n\n");
 
 printf(" Use the Green's theorem to evaluate :   \n\n");  
 
 printf("    (                                (%.1f   (%s\n",    by, veq);
 printf(" int( %s dx + %s dy = int(   int( %s dx dy\n", 
                       Meq, Neq, N_x_mns_M_y_eq);
 printf("    (c                               (%.1f  (%s\n\n\n\n\n", ay, ueq);         
 stop(); 
 
/* --------------------------------- */ 
 clrscrn();
 printf(" The Green's theorem :   \n\n");
 printf("    (                            (b   (v(x)\n" 
        " int( M(x,y) + dx N(x,y) dy = int(  int( (N_x - M_y) dx dy\n"
        "    (c                           (a   (u(x)\n\n\n");
        
 printf(" M(x,y) = %s \n",   Meq);
 printf(" N(x,y) = %s \n\n", Neq);

 
 printf(" N_x_mns_M_y(x,y) = %s  \n\n", N_x_mns_M_y_eq);
 
 printf(" v(x) = %s   \n", veq); 
 printf(" u(x) = %s \n\n", ueq);

 printf(" With simpson_dxdy().\n\n");
 printf("    (%.1f    (%s\n", by, veq);
 printf(" int(    int( %s  dx dy = %.5f\n", N_x_mns_M_y_eq, 
             simpson_dxdy(N_x_mns_M_y, u,v,n, ay,by,ny) );
 printf("    (%.1f   (%s\n\n\n", ay, ueq);

 stop();

 return 0;
}
/* --------------------------------- */
/* --------------------------------- */


On utilise simplement l'intégrale double du théoreme de Green.


Exemple de sortie écran :

 The Green's theorem :   

    (                            (b   (v(x)
 int( M(x,y) + dx N(x,y) dy = int( int( (N_x - M_y) dx dy
    (c                           (a   (u(x) 




 Use the Green's theorem to evaluate :   

    (                                (0.0   (-x
 int( (x**2+y) dx + (x*y**2) dy = int(   int( (y**2)-1 dx dy
    (c                               (-1.0  (x**2




 Press return to continue.

Exemple de sortie écran :

 The Green's theorem :   

    (                            (b   (v(x)
 int( M(x,y) + dx N(x,y) dy = int(  int( (N_x - M_y) dx dy
    (c                           (a   (u(x)


 M(x,y) = (x**2+y) 
 N(x,y) = (x*y**2) 

 N_x_mns_M_y(x,y) = (y**2)-1  

 v(x) = -x   
 u(x) = x**2 

 With simpson_dxdy().

    (0.0    (-x
 int(    int( (y**2)-1  dx dy = -0.11667
    (-1.0   (x**2


 Press return to continue.
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