Unit 5.3 Runga Kutta 2nd Order Method

start
input x,y,h,xf,  initial values, size and required values

while loop until (x<xf)
    s1 = f(x,y);
    s2 = f(x+h,y+(h*s1));
    s = (s1+s2)/2;
    y = y+ (h*s);
    x = x+h;
end while loop

display output y
stop


// Online C compiler to run C program online
#include <stdio.h>
#include<math.h>
#define f(x,y) (x+y)
int main() {
    int n,i;
    float x0,y0,xn,h,s,s1,s2;
     printf("Enter the x0,y0,h & xn\n");
    scanf("%f %f %f %f",&x0,&y0,&h,&xn);

    while(x0<xn){
        s1 = f(x0,y0);
        s2 = f(x0+h,y0+(h*s1));
        s = (s1+s2)/2;
        y0 = y0+ (h*s);
        x0 = x0 + h;
        printf("\ny(%f) =  %f",x0,y0);
    }
    printf("\n\nFinal Output y(%f) =  %f",x0,y0);
}

Enter the x0,y0,h & xn
0 1 0.1 0.4

y(0.100000) =  1.110000
y(0.200000) =  1.242050
y(0.300000) =  1.398465
y(0.400000) =  1.581804

Final Output y(0.400000) =  1.581804
/*
Enter the first and second value
1 2
Enter the length and required result
0.2 1.4
    x0             y0              s1              s2              s
1.200000        2.680000        3.000000        3.800000        3.400000
1.400000        3.553600        3.880000        4.856000        4.368000

Output is 3.553600
*/