/******************************************************************************
This program first defines the function f(x, y), which is the differential
equation that we want to solve. Then, it defines the function
milne_predictor_corrector(), which implements the Milne predictor corrector
method. This function takes in the initial value of x, y, the step size, and
the number of steps, and returns the solution to the differential equation.
*******************************************************************************/
#include <iostream>
#include <math.h>
using namespace std;
double f(double x, double y) {
return x * y;
}
double milne_predictor_corrector(double x0, double y0, double h, int n) {
double y[n + 1];
y[0] = y0;
for (int i = 1; i <= n; i++) {
double y_pred = y[i - 1] + h * f(x0 + (i - 1) * h, y[i - 1]);
double y_corr = y[i - 1] + h * (2 * f(x0 + (i - 1) * h, y[i - 1]) + f(x0 + i * h, y_pred));
y[i] = y_corr / 3;
}
return y[n];
}
int main() {
double x0 = 0;
double y0 = 1;
double h = 0.1;
int n = 10;
double y = milne_predictor_corrector(x0, y0, h, n);
cout << "The solution is y = " << y << endl;
return 0;
}
