用龙格库塔法计算

 

#include <iostream>

#include<iomanip>

#include <cmath>

using namespace std;

int main()

{

      double a = 1, b = 3;      //a,b表示[a,b]求解区间

      double x0 = 1, y0 = 2;      //x0表示初始时刻x的值，y0表示初始时刻y的值

      double x, y;                  //x,y分别表示变化的时候x，y的值

      double F1, F2, F3, F4;      //F1,F2,F3,F4分别表示斜率值

      double h = 1.0f / 128;      //h表示步长

      cout << setiosflags(ios::left)

            << setw(25) << "x的值"

            << setw(25) << "龙格库塔计算得到的值"

            << setw(25) << "解析解得到的值"

            << setw(25) << "误差" << endl;

      x = x0;

      y = y0;

      cout << setw(25) << x

            << setw(25) << y

            << setw(25) << y0

            << setw(25) << abs(y0-y)<< endl;

      do

      {

            F1 = h*pow(x, -2)*(x*y - y*y);

            F2 = h*pow(x + h / 2, -2)*((x + h / 2 )* (y + F1 / 2) - (y + F1 / 2)*(y + F1 / 2));

            F3 = h*pow(x + h / 2, -2)*((x + h / 2)* (y + F2 / 2) - (y + F2 / 2)*(y + F2 / 2));

            F4 = h*pow(x + h, -2)*((x + h)* (y + F3) - (y + F3)*(y + F3));

            y += (F1 + 2 * F2 + 2 * F3 + F4) / 6;

            x = x + h;

            cout<< setw(25) << x

                  << setw(25) << y

                  << setw(25) << x / (1.0f / 2 + log(x))

                  << abs(x / (1.0f / 2 + log(x)) - y) << endl;

      } while (x<=b);

   

      return 0;

}