11 lab numberical methods

run.c

#include <stdio.h>
#include <math.h>

double c = 5;
double x0=0.0;
double y0=1.0;

double f(double x, double y){
	
	return 2 * pow(x, 2) + y;
	
	}
	
double yt(double x){
	
	return c * exp(x) - 2 * pow(x, 2) - 4 * x - 4;
	
	}

double rk(double x,double y,double h){
	
	double k1 = f(x, y);
    double k2 = f(x + h / 2, y + h / 2 * k1);
    double k3 = f(x + h / 2, y + h / 2 * k2);
    double k4 = f(x + h, y + h * k3);
    
    return y + h / 6 * (k1 + 2 * k2 + 2 * k3 + k4);
    
    }
  
double rk2(double x0,double y0, double h) {
	
	double y1=rk(x0,y0,h/2);
	double y2=rk(x0+h/2,y1,h/2);
	
	return y2;
	
   }

int main(int argc, char **argv) {
	
	
	double h=1E-2;
	double xn=10;
	
	
	FILE * file = fopen("out .txt", "wt");
	
	double x1=x0;
	double y1=y0;
	double x2=x0;
	double y2=y0;
	
	do {
		
		x0=x1;
		y0=y1;
		double y00=y2;
		double x1=x0+h;
		double y1=rk(x0,y0,h);
		double y2=rk(x0,y00,h);
		
		
	fprintf(file, "x1=%lf   y1=%lf   eps=%e x2=%lf  y2=%lf eps=%e\n", x1, y1, fabs(y1 - yt(x1)),x2, y2, fabs(16.0/15.0*(y2 - y1)));
	
	}
	
  while (x1 < xn);
  
  fclose(file);
  
  return 0;
}