/* nag_ode_bvp_fd_nonlin_gen (d02rac) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 3, 1992.
* Mark 7 revised, 2001.
* Mark 8 revised, 2004.
*
*/
#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nagd02.h>
#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL fcn(Integer neq, double x, double eps, const double y[],
double f[], Nag_User *comm);
static void NAG_CALL g(Integer neq, double eps, const double ya[],
const double yb[], double bc[], Nag_User *comm);
static void NAG_CALL jaceps(Integer neq, double x, double eps, const double y[],
double f[], Nag_User *comm);
static void NAG_CALL jacgep(Integer neq, double eps, const double ya[],
const double yb[], double bcep[], Nag_User *comm);
static void NAG_CALL jacobf(Integer neq, double x, double eps, const double y[],
double f[], Nag_User *comm);
static void NAG_CALL jacobg(Integer neq, double eps, const double ya[],
const double yb[], double aj[], double bj[],
Nag_User *comm);
#ifdef __cplusplus
}
#endif
#define NEQ 3
#define MNP 40
#define Y(I, J) y[(I) *tdy + J]
int main(void)
{
static Integer use_comm[6] = {1, 1, 1, 1, 1, 1};
double *abt = 0;
double deleps;
double tol;
double *x = 0, *y = 0;
Integer exit_status = 0;
Integer i, j;
Integer np;
Integer numbeg, nummix;
Integer neq, mnp, tdy;
Nag_User comm;
NagError fail;
INIT_FAIL(fail);
printf(
"nag_ode_bvp_fd_nonlin_gen (d02rac) Example Program Results\n");
/* For communication with user-supplied functions: */
comm.p = (Pointer)&use_comm;
printf("\nCalculation using analytic Jacobians\n\n");
neq = NEQ;
mnp = MNP;
if (neq >= 1)
{
if (!(abt = NAG_ALLOC(neq, double)) ||
!(x = NAG_ALLOC(mnp, double)) ||
!(y = NAG_ALLOC(neq*mnp, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
tdy = mnp;
}
else
{
exit_status = 1;
return exit_status;
}
tol = 1.0e-4;
np = 17;
numbeg = 2;
nummix = 0;
x[0] = 0.0;
x[np-1] = 10.0;
deleps = 0.1;
/* nag_ode_bvp_fd_nonlin_gen (d02rac).
* Ordinary differential equations solver, for general
* nonlinear two-point boundary value problems, using a
* finite difference technique with deferred correction
*/
nag_ode_bvp_fd_nonlin_gen(neq, &deleps, fcn, numbeg, nummix, g,
Nag_DefInitMesh, mnp, &np, x, y, tol, abt, jacobf,
jacobg, jaceps, jacgep, &comm, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_ode_bvp_fd_nonlin_gen (d02rac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
printf("Solution on final mesh of %ld points \n", np);
printf(" X Y(1) Y(2) Y(3)\n");
for (j = 0; j < np; ++j)
{
printf(" %9.3f ", x[j]);
for (i = 0; i < neq; ++i)
printf(" %9.4f", Y(i, j));
printf("\n");
}
printf("\n\nMaximum estimated error by components \n");
for (i = 1; i <= 3; ++i)
printf(" %11.2e", abt[i-1]);
printf(" \n");
END:
NAG_FREE(abt);
NAG_FREE(x);
NAG_FREE(y);
return exit_status;
}
#undef Y
static void NAG_CALL fcn(Integer neq, double x, double eps, const double y[],
double f[], Nag_User *comm)
{
Integer *use_comm = (Integer *)comm->p;
if (use_comm[0])
{
printf("(User-supplied callback fcn, first invocation.)\n");
use_comm[0] = 0;
}
f[0] = y[1];
f[1] = y[2];
f[2] = -y[0] * y[2] - (1.0 - y[1]*y[1])*2.0*eps;
}
static void NAG_CALL g(Integer neq, double eps, const double ya[],
const double yb[], double bc[], Nag_User *comm)
{
Integer *use_comm = (Integer *)comm->p;
if (use_comm[1])
{
printf("(User-supplied callback g, first invocation.)\n");
use_comm[1] = 0;
}
bc[0] = ya[0];
bc[1] = ya[1];
bc[2] = yb[1] - 1.0;
} /* g */
static void NAG_CALL jaceps(Integer neq, double x, double eps, const double y[],
double f[], Nag_User *comm)
{
Integer *use_comm = (Integer *)comm->p;
if (use_comm[2])
{
printf("(User-supplied callback jaceps, first invocation.)\n");
use_comm[2] = 0;
}
f[0] = 0.0;
f[1] = 0.0;
f[2] = (1.0 - y[1]*y[1]) * -2.0;
}
static void NAG_CALL jacgep(Integer neq, double eps, const double ya[],
const double yb[], double bcep[], Nag_User *comm)
{
Integer i;
Integer *use_comm = (Integer *)comm->p;
if (use_comm[3])
{
printf("(User-supplied callback jacgep, first invocation.)\n");
use_comm[3] = 0;
}
for (i = 0; i < neq; ++i)
bcep[i] = 0.0;
}
static void NAG_CALL jacobf(Integer neq, double x, double eps, const double y[],
double f[], Nag_User *comm)
{
Integer i, j;
Integer *use_comm = (Integer *)comm->p;
#define Y(I) y[(I) -1]
#define F(I, J) f[((I) -1)*neq+(J) -1]
if (use_comm[4])
{
printf("(User-supplied callback jacobf, first invocation.)\n");
use_comm[4] = 0;
}
for (i = 1; i <= neq; ++i)
{
for (j = 1; j <= neq; ++j)
F(i, j) = 0.0;
}
F(1, 2) = 1.0;
F(2, 3) = 1.0;
F(3, 1) = -Y(3);
F(3, 2) = Y(2) * 4.0 * eps;
F(3, 3) = -Y(1);
}
static void NAG_CALL jacobg(Integer neq, double eps, const double ya[],
const double yb[], double aj[], double bj[],
Nag_User *comm)
{
Integer i, j;
Integer *use_comm = (Integer *)comm->p;
#define YA(I) ya[(I) -1]
#define YB(I) yb[(I) -1]
#define AJ(I, J) aj[((I) -1)*neq+(J) -1]
#define BJ(I, J) bj[((I) -1)*neq+(J) -1]
if (use_comm[5])
{
printf("(User-supplied callback jacobg, first invocation.)\n");
use_comm[5] = 0;
}
for (i = 1; i <= neq; ++i)
for (j = 1; j <= neq; ++j)
{
AJ(i, j) = 0.0;
BJ(i, j) = 0.0;
}
AJ(1, 1) = 1.0;
AJ(2, 2) = 1.0;
BJ(3, 2) = 1.0;
}