GSL 自适应积分给出无效指针错误

Question

我正在尝试使用内置的 RK2imp 方法来解决GSL 示例示例中给出的使用自适应求解器进行集成的范德波尔问题的略微修改版本。 但是，我不断收到此“错误：无效指针”。 我在这里附上我的代码

#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_odeiv2.h>

#define ABTOL 1e-18

#define A 2.00861986087484313650940188
#define mu 1.0
#define TEND 6.6632868593231301896996820305

double eps_abs=ABTOL, eps_rel=0.0, tend=TEND;

int func (double t, const double y[], double f[], void *params)
{
    (void)(t); /* avoid unused parameter warning */
    f[0] = y[1];
    f[1] = -y[0] - mu*y[1]*(y[0]*y[0] - 1);
    return GSL_SUCCESS;
}

int jac (double t, const double y[], double *dfdy, double dfdt[], void *params)
{
    (void)(t); /* avoid unused parameter warning */
    gsl_matrix_view dfdy_mat = gsl_matrix_view_array (dfdy, 2, 2);
    gsl_matrix * m = &dfdy_mat.matrix;
    gsl_matrix_set (m, 0, 0, 0.0);
    gsl_matrix_set (m, 0, 1, 1.0);
    gsl_matrix_set (m, 1, 0, -2.0*mu*y[0]*y[1] - 1.0);
    gsl_matrix_set (m, 1, 1, -mu*(y[0]*y[0] - 1.0));
    dfdt[0] = 0.0;
    dfdt[1] = 0.0;
    return GSL_SUCCESS;
}

int main (void)
{
    const gsl_odeiv2_step_type * T = gsl_odeiv2_step_rk2imp;

    gsl_odeiv2_step * s = gsl_odeiv2_step_alloc (T, 2);
    gsl_odeiv2_control * c = gsl_odeiv2_control_y_new (eps_abs, eps_rel);
    gsl_odeiv2_evolve * e = gsl_odeiv2_evolve_alloc (2);

    gsl_odeiv2_system sys = {func, jac, 2, NULL};

    double t = 0.0, t1 = TEND;
    double h = 1e-6;
    double y[2] = { A, 0.0 };

    while (t < t1)
    {
        int status = gsl_odeiv2_evolve_apply (e, c, s, &sys, &t, t1, &h, y);

        if (status != GSL_SUCCESS)
        {
            printf ("error: %s\n", gsl_strerror (status));
            break;
        }

        printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
    }

    gsl_odeiv2_evolve_free (e);
    gsl_odeiv2_control_free (c);
    gsl_odeiv2_step_free (s);
    return 0;
}
 

这是我得到的 output：

 error: invalid pointer

我知道我可能会犯一个非常简单（而且很愚蠢）的错误，但由于某种原因我看不到它。 我真的很感激任何帮助。 谢谢你。

Answer 1

据我了解，不适当的步进 function 用于数值积分方法 (Runge-Kutta)。 这里最好使用显式方法，甚至可以使用gsl_odeiv2_step_rk2步进 function，但解会收敛很长时间。 或者您可以使用隐式集成方法，但您需要使用步进驱动程序 ：

#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_odeiv2.h>

#define ABTOL 1e-18

#define A 2.00861986087484313650940188
#define mu 1.0
#define TEND 6.6632868593231301896996820305

double eps_abs=ABTOL, eps_rel=0.0, tend=TEND;

int func (double t, const double y[], double f[], void *params)
{
    (void)(t); /* avoid unused parameter warning */
    f[0] = y[1];
    f[1] = -y[0] - mu*y[1]*(y[0]*y[0] - 1);
    return GSL_SUCCESS;
}

int jac (double t, const double y[], double *dfdy, double dfdt[], void *params)
{
    (void)(t); /* avoid unused parameter warning */
    gsl_matrix_view dfdy_mat = gsl_matrix_view_array (dfdy, 2, 2);
    gsl_matrix * m = &dfdy_mat.matrix;
    gsl_matrix_set (m, 0, 0, 0.0);
    gsl_matrix_set (m, 0, 1, 1.0);
    gsl_matrix_set (m, 1, 0, -2.0*mu*y[0]*y[1] - 1.0);
    gsl_matrix_set (m, 1, 1, -mu*(y[0]*y[0] - 1.0));
    dfdt[0] = 0.0;
    dfdt[1] = 0.0;
    return GSL_SUCCESS;
}

int main (void)
{
    const gsl_odeiv2_step_type * T = gsl_odeiv2_step_msadams;
    // with "gsl_odeiv2_step_rk2imp" stepping function the solution
    // converges VERY SLOWLY and may be "failure" error at the end

    gsl_odeiv2_step * s = gsl_odeiv2_step_alloc (T, 2);
    gsl_odeiv2_control * c = gsl_odeiv2_control_y_new (eps_abs, eps_rel);
    gsl_odeiv2_evolve * e = gsl_odeiv2_evolve_alloc (2);

    gsl_odeiv2_system sys = {func, jac, 2, NULL};

    gsl_odeiv2_driver * d = gsl_odeiv2_driver_alloc_y_new(&sys, T, 1e-6, 1e-6, 1e-6 );
    gsl_odeiv2_step_set_driver(s, d);

    double t = 0.0, t1 = TEND;
    double h = 1e-6;
    double y[2] = { A, 0.0 };

    while (t < t1)
    {
        int status = gsl_odeiv2_evolve_apply (e, c, s, &sys, &t, t1, &h, y);

        if (status != GSL_SUCCESS)
        {
            printf ("error: %s\n", gsl_strerror (status));
            break;
        }

        printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
    }

    gsl_odeiv2_evolve_free (e);
    gsl_odeiv2_control_free (c);
    gsl_odeiv2_step_free (s);
    return 0;
}