求解常微分方程初值问题之改进Euler法：预报-校正公式

//实现Euler预报_校正法

#include <iostream>

#include <math.h>

#include <iomanip>

using namespace std;

class euler

{

private:

int i, n;

double f, h, x, x_last, yc, yp;

public:

double func(double z, double t)

{

f = (1 + z) * t * t / 2;

return f;

}

void pc();

};

void main()

{

euler predictor_corrector;

predictor_corrector.pc();

}

void euler::pc()

{

cout << "\n输入初始条件：" << endl;

cout << "\n输入x0：";

cin >> x;

cout << "\n输入y0：";

cin >> yc;

cout << "\n输入y需要的x值：";

cin >> x_last;

cout << "\n输入等分数：";

cin >> n;

h = (x_last - x) / n;

for (i = 0; i < n; i++)

{

yp = yc + h * func(x, yc);

yc += 0.5 * h * (func(x, yc) + func((x + h), yp));

x += h;

cout.precision(10);

cout << x << setw(15) << yc << endl;

}

}