/* nag_ode_bvp_coll_nlin_solve (d02tlc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.3, 2022.
*/
#include <math.h>
#include <nag.h>
#include <stdio.h>
typedef struct {
double omega;
double sqrofr;
} func_data;
#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL ffun(double x, const double y[], Integer neq,
const Integer m[], double f[], Nag_Comm *comm);
static void NAG_CALL fjac(double x, const double y[], Integer neq,
const Integer m[], double dfdy[], Nag_Comm *comm);
static void NAG_CALL gafun(const double ya[], Integer neq, const Integer m[],
Integer nlbc, double ga[], Nag_Comm *comm);
static void NAG_CALL gbfun(const double yb[], Integer neq, const Integer m[],
Integer nrbc, double gb[], Nag_Comm *comm);
static void NAG_CALL gajac(const double ya[], Integer neq, const Integer m[],
Integer nlbc, double dgady[], Nag_Comm *comm);
static void NAG_CALL gbjac(const double yb[], Integer neq, const Integer m[],
Integer nrbc, double dgbdy[], Nag_Comm *comm);
static void NAG_CALL guess(double x, Integer neq, const Integer m[], double y[],
double dym[], Nag_Comm *comm);
#ifdef __cplusplus
}
#endif
int main(void) {
/* Scalars */
double one = 1.0;
Integer exit_status = 0, neq = 3, mmax = 3, nlbc = 3, nrbc = 3;
double dx, ermx, r, omega;
Integer i, iermx, ijermx, j, k, licomm, lrcomm, mxmesh, ncol, ncont, nmesh;
/* Arrays */
static double ruser[7] = {-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0};
double rdum[1];
Integer idum[2];
double *mesh = 0, *tol = 0, *rcomm = 0, *y = 0;
Integer *ipmesh = 0, *icomm = 0, *m = 0;
func_data fd;
/* Nag Types */
Nag_Comm comm;
NagError fail;
INIT_FAIL(fail);
printf("nag_ode_bvp_coll_nlin_solve (d02tlc) Example Program Results\n\n");
/* For communication with user-supplied functions: */
comm.user = ruser;
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &ncol, &nmesh,
&mxmesh);
if (!(mesh = NAG_ALLOC(mxmesh, double)) || !(m = NAG_ALLOC(neq, Integer)) ||
!(tol = NAG_ALLOC(neq, double)) || !(y = NAG_ALLOC(neq * mmax, double)) ||
!(ipmesh = NAG_ALLOC(mxmesh, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Set problem equation orders. */
m[0] = 1;
m[1] = 3;
m[2] = 2;
scanf("%lf%*[^\n] ", &omega);
for (i = 0; i < neq; i++)
scanf("%lf", &tol[i]);
scanf("%*[^\n] ");
dx = one / (double)(nmesh - 1);
mesh[0] = 0.0;
ipmesh[0] = 1;
for (i = 1; i < nmesh - 1; i++) {
mesh[i] = mesh[i - 1] + dx;
ipmesh[i] = 2;
}
mesh[nmesh - 1] = one;
ipmesh[nmesh - 1] = 1;
/* Query to get size of rcomm and icomm (by setting lrcomm=0) */
/* nag_ode_bvp_coll_nlin_setup (d02tvc).
* Ordinary differential equations, general nonlinear boundary value problem,
* setup for nag_ode_bvp_coll_nlin_solve (d02tlc).
*/
nag_ode_bvp_coll_nlin_setup(neq, m, nlbc, nrbc, ncol, tol, mxmesh, nmesh,
mesh, ipmesh, rdum, 0, idum, 2, &fail);
if (fail.code == NE_NOERROR) {
lrcomm = idum[0];
licomm = idum[1];
printf("lrcomm = %" NAG_IFMT ", licomm = %" NAG_IFMT "\n", lrcomm, licomm);
if (!(rcomm = NAG_ALLOC(lrcomm, double)) ||
!(icomm = NAG_ALLOC(licomm, Integer))) {
printf("Allocation failure\n");
exit_status = -2;
goto END;
}
/* Initialize again using nag_ode_bvp_coll_nlin_setup (d02tvc). */
nag_ode_bvp_coll_nlin_setup(neq, m, nlbc, nrbc, ncol, tol, mxmesh, nmesh,
mesh, ipmesh, rcomm, lrcomm, icomm, licomm,
&fail);
}
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_bvp_coll_nlin_setup (d02tvc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Number of continuation steps (last r=100**ncont, sqrofr=10**ncont) */
scanf("%" NAG_IFMT "%*[^\n] ", &ncont);
/* Initialize problem continuation parameter. */
scanf("%lf%*[^\n] ", &r);
/* Set data required for the user-supplied functions */
fd.omega = omega;
fd.sqrofr = sqrt(r);
/* Associate the data structure with comm.p */
comm.p = (Pointer)&fd;
for (j = 0; j < ncont; j++) {
printf("\n Tolerance = %8.1e r = %10.3e\n", tol[0], r);
/* Solve problem. */
/* nag_ode_bvp_coll_nlin_solve (d02tlc).
* Ordinary differential equations, general nonlinear boundary value
* problem, collocation technique.
*/
nag_ode_bvp_coll_nlin_solve(ffun, fjac, gafun, gbfun, gajac, gbjac, guess,
rcomm, icomm, &comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_bvp_coll_nlin_solve (d02tlc).\n%s\n",
fail.message);
exit_status = 2;
goto END;
}
/* Extract mesh */
/* nag_ode_bvp_coll_nlin_diag (d02tzc).
* Ordinary differential equations, general nonlinear boundary value
* problem, diagnostics for nag_ode_bvp_coll_nlin_solve (d02tlc).
*/
nag_ode_bvp_coll_nlin_diag(mxmesh, &nmesh, mesh, ipmesh, &ermx, &iermx,
&ijermx, rcomm, icomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_bvp_coll_nlin_diag (d02tzc).\n%s\n",
fail.message);
exit_status = 3;
goto END;
}
/* Print mesh and error statistics. */
printf("\n Used a mesh of %4" NAG_IFMT " points\n", nmesh);
printf(" Maximum error = %10.2e in interval %4" NAG_IFMT " for component"
" %4" NAG_IFMT "\n\n\n",
ermx, iermx, ijermx);
printf(" Mesh points:\n");
for (i = 0; i < nmesh; i++) {
printf("%4" NAG_IFMT "(%1" NAG_IFMT ")", i + 1, ipmesh[i]);
printf("%12.4e%s", mesh[i], i % 4 == 3 ? "\n" : " ");
}
/* Print solution components on mesh. */
printf("\n\n x f f' g\n");
for (i = 0; i < nmesh; i++) {
/* nag_ode_bvp_coll_nlin_interp (d02tyc).
* Ordinary differential equations, general nonlinear boundary value
* problem, interpolation for nag_ode_bvp_coll_nlin_solve (d02tlc).
*/
nag_ode_bvp_coll_nlin_interp(mesh[i], y, neq, mmax, rcomm, icomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_bvp_coll_nlin_interp (d02tyc).\n%s\n",
fail.message);
exit_status = 4;
goto END;
}
printf("%8.3f ", mesh[i]);
for (k = 0; k < neq; k++)
printf("%9.4f", y[k]);
printf("\n");
}
if (j == ncont - 1) {
goto END;
}
/* Modify continuation parameter. */
r = 100.0 * r;
fd.sqrofr = sqrt(r);
/* Select mesh for continuation and call continuation primer routine. */
for (i = 1; i < nmesh - 1; i++) {
ipmesh[i] = 2;
}
/* nag_ode_bvp_coll_nlin_contin (d02txc).
* Ordinary differential equations, general nonlinear boundary value
* problem, continuation facility for nag_ode_bvp_coll_nlin_solve (d02tlc).
*/
nag_ode_bvp_coll_nlin_contin(mxmesh, nmesh, mesh, ipmesh, rcomm, icomm,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_bvp_coll_nlin_contin (d02txc).\n%s\n",
fail.message);
exit_status = 5;
goto END;
}
}
END:
NAG_FREE(mesh);
NAG_FREE(m);
NAG_FREE(tol);
NAG_FREE(rcomm);
NAG_FREE(y);
NAG_FREE(ipmesh);
NAG_FREE(icomm);
return exit_status;
}
static void NAG_CALL ffun(double x, const double y[], Integer neq,
const Integer m[], double f[], Nag_Comm *comm) {
func_data *fd = (func_data *)comm->p;
double y22 = y[1 + 2 * neq];
double y31 = y[2 + 1 * neq];
if (comm->user[0] == -1.0) {
printf("(User-supplied callback ffun, first invocation.)\n");
comm->user[0] = 0.0;
}
f[0] = y[1];
f[1] = -(y[0] * y22 + y[2] * y31) * fd->sqrofr;
f[2] = (y[1] * y[2] - y[0] * y31) * fd->sqrofr;
}
static void NAG_CALL fjac(double x, const double y[], Integer neq,
const Integer m[], double dfdy[], Nag_Comm *comm) {
func_data *fd = (func_data *)comm->p;
double y22 = y[1 + 2 * neq];
double y31 = y[2 + 1 * neq];
if (comm->user[1] == -1.0) {
printf("(User-supplied callback fjac, first invocation.)\n");
comm->user[1] = 0.0;
}
dfdy[0 + 1 * neq + 0 * neq * neq] = 1.0;
dfdy[1 + 0 * neq + 0 * neq * neq] = -y22 * fd->sqrofr;
dfdy[1 + 1 * neq + 2 * neq * neq] = -y[0] * fd->sqrofr;
dfdy[1 + 2 * neq + 0 * neq * neq] = -y31 * fd->sqrofr;
dfdy[1 + 2 * neq + 1 * neq * neq] = -y[2] * fd->sqrofr;
dfdy[2 + 0 * neq + 0 * neq * neq] = -y31 * fd->sqrofr;
dfdy[2 + 1 * neq + 0 * neq * neq] = y[2] * fd->sqrofr;
dfdy[2 + 2 * neq + 0 * neq * neq] = y[1] * fd->sqrofr;
dfdy[2 + 2 * neq + 1 * neq * neq] = -y[0] * fd->sqrofr;
}
static void NAG_CALL gafun(const double ya[], Integer neq, const Integer m[],
Integer nlbc, double ga[], Nag_Comm *comm) {
func_data *fd = (func_data *)comm->p;
if (comm->user[2] == -1.0) {
printf("(User-supplied callback gafun, first invocation.)\n");
comm->user[2] = 0.0;
}
ga[0] = ya[0];
ga[1] = ya[1];
ga[2] = ya[2] - fd->omega;
}
static void NAG_CALL gbfun(const double yb[], Integer neq, const Integer m[],
Integer nrbc, double gb[], Nag_Comm *comm) {
func_data *fd = (func_data *)comm->p;
if (comm->user[3] == -1.0) {
printf("(User-supplied callback gbfun, first invocation.)\n");
comm->user[3] = 0.0;
}
gb[0] = yb[0];
gb[1] = yb[1];
gb[2] = yb[2] + fd->omega;
}
static void NAG_CALL gajac(const double ya[], Integer neq, const Integer m[],
Integer nlbc, double dgady[], Nag_Comm *comm) {
if (comm->user[4] == -1.0) {
printf("(User-supplied callback gajac, first invocation.)\n");
comm->user[4] = 0.0;
}
dgady[0 + 0 * neq] = 1.0;
dgady[1 + 1 * neq] = 1.0;
dgady[2 + 2 * neq] = 1.0;
}
static void NAG_CALL gbjac(const double yb[], Integer neq, const Integer m[],
Integer nrbc, double dgbdy[], Nag_Comm *comm) {
if (comm->user[5] == -1.0) {
printf("(User-supplied callback gbjac, first invocation.)\n");
comm->user[5] = 0.0;
}
dgbdy[0 + 0 * neq] = 1.0;
dgbdy[1 + 1 * neq] = 1.0;
dgbdy[2 + 2 * neq] = 1.0;
}
static void NAG_CALL guess(double x, Integer neq, const Integer m[], double y[],
double dym[], Nag_Comm *comm) {
func_data *fd = (func_data *)comm->p;
double xh = x - 0.5;
double xx1 = x * (x - 1.0);
if (comm->user[6] == -1.0) {
printf("(User-supplied callback guess, first invocation.)\n");
comm->user[6] = 0.0;
}
y[0 + 0 * neq] = -xh * pow(xx1, 2);
y[1 + 0 * neq] = -xx1 * (5.0 * xx1 + 1.0);
y[1 + 1 * neq] = -2.0 * xh * (10.0 * xx1 + 1.0);
y[1 + 2 * neq] = -12.0 * (5.0 * xx1 + x);
y[2 + 0 * neq] = -8.0 * fd->omega * pow(xh, 3);
y[2 + 1 * neq] = -24.0 * fd->omega * pow(xh, 2);
dym[0] = y[1];
dym[1] = -120.0 * xh;
dym[2] = -48.0 * fd->omega * xh;
}