//實現Milne預報-校正法
#include <iostream>
#include <math.h>
#include <iomanip>
using namespace std;
class milne
{
private:
int i, n;
double f, h, x, x_last, y, y1, y2, y3, yc, yp;
double f0, f1, f2;
public:
double func(double z, double t)
{
f = -t + sin(z);
return f;
}
void pc();
};
void main()
{
milne cotes_pc;
cotes_pc.pc();
}
void milne::pc()
{
cout << "\n輸入初始條件:";
cout << "\n輸入x0:";
cin >> x;
cout << "\n輸入y0:";
cin >> y;
cout << "\n輸入y需要的x值:";
cin >> x_last;
cout << "\n輸入等分數:";
cin >> n;
h = (x_last - x) / n;
cout << "\n輸入在x = " << (x - h) << "處的y(-1):";
cin >> y1;
cout << "\n輸入在x = " << (x - 2 * h) << "處的y(-2):";
cin >> y2;
cout << "\n輸入在x = " << (x - 3 * h) << "處的y(-3):";
cin >> y3;
f0 = func(x, y);
f1 = func((x - h), y1);
f2 = func((x - 2 * h), y2);
for (i = 0; i < n; i++)
{
yp = y3 + (4 * h / 3) * (2 * f2 - f1 + 2 * f0);
y3 = y2;
y2 = y1;
y1 = y;
y = y2 + (h / 3) * (f1 + 4 * f0 + func((x + h), yp));
f2 = f1;
f1 = f0;
x += h;
f0 = func(x, y);
cout << x << setw(15) << y << endl;
}
}