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/* This file is part of the GNU plotutils package. */
/*
* Copyright (C) 1982-1994, Nicholas B. Tufillaro. All rights reserved.
*
* GNU enhancements Copyright (C) 1996, 1997, 2005, 2008, Free Software
* Foundation, Inc.
*/
/*
* Fifth-Order Runge-Kutta-Fehlberg with adaptive step size
*
*/
#include "sys-defines.h"
#include "ode.h"
#include "extern.h"
#include "num.h"
#define T_LT_TSTOP (tstep>0 ? t<tstop : t>tstop)
void
rka (void)
{
bool gdval = true; /* good value to print ? */
int overtime = 1;
double prevstep = 0.0;
double t;
for (it = 0, t = tstart; T_LT_TSTOP || overtime--; )
{
symtab->sy_value = symtab->sy_val[0] = t;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_val[0] = fsp->sy_value;
fsp->sy_pri[0] = fsp->sy_prime;
}
if (gdval)
printq(); /* output */
if (tstep * (t+tstep-tstop) > 0)
tstep = tstop - t;
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[0] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0]
+ C20 * fsp->sy_k[0];
}
symtab->sy_value = t + C2t * tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[1] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0]
+ (C30 * fsp->sy_k[0]
+ C31 * fsp->sy_k[1]);
}
symtab->sy_value = t + C3t * tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[2] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0]
+ (C40 * fsp->sy_k[0]
+ C41 * fsp->sy_k[1]
+ C42 * fsp->sy_k[2]);
}
symtab->sy_value = t + C4t * tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[3] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0]
+ (C50 * fsp->sy_k[0]
+ C51 * fsp->sy_k[1]
+ C52 * fsp->sy_k[2]
+ C53 * fsp->sy_k[3]);
}
symtab->sy_value = t + tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_k[4] = tstep * fsp->sy_prime;
fsp->sy_value = fsp->sy_val[0]
+ (C60 * fsp->sy_k[0]
+ C61 * fsp->sy_k[1]
+ C62 * fsp->sy_k[2]
+ C63 * fsp->sy_k[3]
+ C64 * fsp->sy_k[4]);
}
symtab->sy_value = t + C6t * tstep;
field();
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
fsp->sy_k[5] = tstep * fsp->sy_prime;
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
{
fsp->sy_predi = fsp->sy_val[0]
+ (A0 * fsp->sy_k[0]
+ A2 * fsp->sy_k[2]
+ A3 * fsp->sy_k[3]
+ A4 * fsp->sy_k[4]);
fsp->sy_value = fsp->sy_val[0]
+ (B0 * fsp->sy_k[0]
+ B2 * fsp->sy_k[2]
+ B3 * fsp->sy_k[3]
+ B4 * fsp->sy_k[4]
+ B5 * fsp->sy_k[5]);
if (fsp->sy_value != 0.0)
fsp->sy_sserr = fabs(1.0 - fsp->sy_predi / fsp->sy_value);
fsp->sy_aberr = fabs(fsp->sy_value - fsp->sy_predi);
}
if (!conflag && T_LT_TSTOP)
{
maxerr();
if (hierror())
{
tstep *= HALF;
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
fsp->sy_value = fsp->sy_val[0];
gdval = false;
continue;
}
else
if (lowerror() && prevstep != tstep)
{
prevstep = tstep; /* prevent infinite loops */
tstep *= TWO;
for (fsp = dqueue; fsp != NULL; fsp = fsp->sy_link)
fsp->sy_value = fsp->sy_val[0];
gdval = false;
continue;
}
}
gdval = true;
prevstep = 0.0;
++it;
t += tstep; /* the roundoff error is gross */
}
}
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