/* ---------------------------------------------------------------------- */
LDBLE
qromb_midpnt (LDBLE x1, LDBLE x2)
/* ---------------------------------------------------------------------- */
{
LDBLE ss, dss;
LDBLE sv[MAX_QUAD + 2], h[MAX_QUAD + 2];
int j;
h[0] = 1.0;
sv[0] = midpnt (x1, x2, 1);
for (j = 1; j < MAX_QUAD; j++)
{
sv[j] = midpnt (x1, x2, j + 1);
h[j] = h[j - 1] / 9.0;
if (fabs (sv[j] - sv[j - 1]) <= G_TOL * fabs (sv[j]))
{
sv[j] *= surface_charge_ptr->grams * surface_charge_ptr->specific_area * alpha / F_C_MOL; /* (ee0RT/2)**1/2, (L/mol)**1/2 C / m**2 */
if ((x2 - 1) < 0.0)
sv[j] *= -1.0;
if (debug_diffuse_layer == TRUE)
{
output_msg (OUTPUT_MESSAGE, "Iterations in qromb_midpnt: %d\n", j);
}
return (sv[j]);
}
if (j >= K_POLY - 1)
{
polint (&h[j - K_POLY], &sv[j - K_POLY], K_POLY, 0.0, &ss, &dss);
if (fabs (dss) <= G_TOL * fabs (ss) || fabs (dss) < G_TOL)
{
ss *= surface_charge_ptr->grams * surface_charge_ptr->specific_area * alpha / F_C_MOL; /* (ee0RT/2)**1/2, (L/mol)**1/2 C / m**2 */
if ((x2 - 1) < 0.0)
ss *= -1.0;
if (debug_diffuse_layer == TRUE)
{
output_msg (OUTPUT_MESSAGE, "Iterations in qromb_midpnt: %d\n", j);
}
return (ss);
}
}
}
sprintf (error_string,
"\nToo many iterations integrating diffuse layer.\n");
error_msg (error_string, STOP);
return (-999.9);
}
double midpnt(double (*func)(double), double a, double b, int n){
double x,tnm,sum,del,ddel;
static double s;
int it,j;
if(n==1){
s=(b-a)*FUNC(0.5*(a+b));
return s;
} else {
for(it=1,j=1;j<n-1;j++) it*=3;
tnm=it;
del=(b-a)/(3.0*tnm);
ddel=del+del;
x=a+0.5*del;
sum=0.0;
for(j=1;j<=it;j++) {
sum+=FUNC(x);
x+=ddel;
sum+=FUNC(x);
x+=del;
}
s=( midpnt(func,a,b,n-1) + (b-a)*sum/tnm )/3.0;
return s;
}
}
int main(void)
{
float a=0.0,b=1.0,s;
int i;
printf("\nIntegral of func computed with MIDPNT\n");
printf("Actual value of integral is %7.4f\n",(fint(b)-fint(a)));
printf("%6s %29s \n","n","Approx. integral");
for (i=1;i<=NMAX;i++) {
s=midpnt(func,a,b,i);
printf("%6d %24.6f\n",i,s);
}
return 0;
}
