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Adam_Bashforth.c
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Adam_Bashforth.c
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#include <stdio.h>
// Function to compute the derivative y'
double derivative(double x, double y)
{
return (x + y) / 2.0;
}
// Adams-Bashforth Predictor
double adams_bashforth_predictor(double yn, double yn_1, double yn_2, double yn_3, double h) {
return yn + h / 24.0 * (55 * derivative(1.5, yn) - 59 * derivative(1.0, yn_1) + 37 * derivative(0.5, yn_2) - 9 * derivative(0.0, yn_3));
}
// Adams-Bashforth Corrector
double adams_bashforth_corrector(double yn, double yn_1, double yn_2, double yn_3, double ynp, double h)
{
return yn + h / 24.0 * (9 * derivative(2.0, ynp) + 19 * derivative(1.5, yn) - 5 * derivative(1.0, yn_1) + derivative(0.5, yn_2));
}
int main() {
double x[4];
double y[4];
double h;
// Input values
printf("Enter the values of x and y:\n");
for (int i = 0; i < 4; i++) {
printf("x%d: ", i);
scanf("%lf", &x[i]);
printf("y%d: ", i);
scanf("%lf", &y[i]);
}
// Input step size
printf("Enter the step size (h): ");
scanf("%lf", &h);
// Predictor
double ynp = adams_bashforth_predictor(y[3], y[2], y[1], y[0], h);
printf("Predicted y(2) = %.4lf\n", ynp);
// Corrector
double ync = adams_bashforth_corrector(y[3], y[2], y[1], y[0], ynp, h);
printf("Corrected y(2) = %.4lf\n", ync);
return 0;
}