求解常微分方程初值问题之Runge_Kutta_Fehlberg法

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//用Runge_Kutta_Fehlberg法求解微分方程
#include <iostream>
#include <math.h>
#include <iomanip>
#include <fstream>

using namespace std;

class rkf
{
private:
int flag;
double eps, error, f, h, hnew, x, xf, y, yold;
double k1, k2, k3, k4, k5, k6;

public:
rkf()
{
  flag = 0;
}
double func(double z, double t)
{
  f = t * t - t * t * t;
  return f;
}
void step_adjust();
double cash_karp(double, double, double);
};

void main()
{
rkf fehlberg;
fehlberg.step_adjust();
}

void rkf::step_adjust()
{
cout << "\n输入x0：";
cin >> x;
cout << "\n输入y0：";
cin >> y;
cout << "\n输入xf：";
cin >> xf;
cout << "\n输入eps：";
cin >> eps;
h = xf - x;
eps = fabs(eps);
ofstream fout("Fehlberg.txt");
fout.precision(4);
cout.precision(4);
do
{
  yold = y;
  y = cash_karp(x, yold, h);
  if (error > eps)
  {
   do
   {
    hnew = h * pow(eps / error, 0.25);
    y = cash_karp(x, yold, hnew);
    h = hnew;
   }while (error > eps);
  }
  else
  {
   do
   {
    hnew = h * pow(eps / error, 0.2);
    y = cash_karp(x, yold, hnew);
    if (error < eps)
    {
     h = hnew;
    }
    else
    {
     y = cash_karp(x, yold, h);
     break;
    }
   }while (error < eps);
  }
  if ((x + h) >= xf)
  {
   h = xf - x;
   y = cash_karp(x, yold, h);
   flag = 1;
  }
  cout << (x + h) << setw(10) << y << setw(15) << error << endl;
  fout << (x + h) << setw(10) << y << setw(15) << error << endl;
  x += h;
}while (flag == 0);
fout.close();
}

double rkf::cash_karp(double p, double q, double r)
{
k1 = r * func(p, q);
k2 = r * func((p + r / 5), (q + k1 / 5));
k3 = r * func((p + 3 * r / 10), (q + 3 * k1 / 40 + 9 * k2 / 40));
k4 = r * func((p + 3 * r / 5), (q + 3 * k1 / 10 - 9 * k2 / 10 + 6 * k3 / 5));
k5 = r * func((p + r), (q - 11 * k1 / 54 + 5 * k2 / 2 - 70 * k3 / 27 + 35 * k4 / 27));
k6 = r * func((p + 7 * r / 8), (q + 1631 * k1 / 55296 + 175 * k2 / 512 + 575 * k3 / 13824 + 44275 * k4 / 110592 + 253 * k5 / 4096));
q += 37 * k1 / 378 + 250 * k3 / 621 + 125 * k4 / 594 + 512 * k6 / 1771;
error = fabs(k1 * (2825.0 / 27648 - 37.0 / 378) + k3 * (18575.0 / 48384 - 250.0 / 621) + k4 * (13525.0 / 55296 - 125.0 / 594) + (k5 * 277 / 14336) + k6 * (1.0 / 4 - 512.0 / 1771));
return q;
}