Question

You are required to develop a computer code that that can solve systems of ODE. The code should request the user to choose one of the following methods for solving the system:

? Euler

? 4th Order Runge Kutta  

Answer 1

For ODE ...

1). EULAR'S METHOD C-CODE :

"

#include<stdio.h>

float fun(float x,float y)

{

    float f;

    f=x+y;

    return f;

}

main()

{

    float a,b,x,y,h,t,k;

    printf("\nEnter x0,y0,h,xn: ");

    scanf("%f%f%f%f",&a,&b,&h,&t);

    x=a;

    y=b;

    printf("\n  x\t  y\n");

    while(x<=t)

    {

        k=h*fun(x,y);

        y=y+k;

        x=x+h;

        printf("%0.3f\t%0.3f\n",x,y);

    }

} "

2). 4TH ORDER RUNGE KUTTA METHOD C-CODE :

"
#include<stdio.h>
#include<math.h>
float f(float x,float y);
int main()
{
    float x0,y0,m1,m2,m3,m4,m,y,x,h,xn;
    printf("Enter x0,y0,xn,h:");
    scanf("%f %f %f %f",&x0,&y0,&xn,&h);
    x=x0;
    y=y0;
    printf("\n\nX\t\tY\n");
    while(x<xn)
    {
        m1=f(x0,y0);
        m2=f((x0+h/2.0),(y0+m1*h/2.0));
        m3=f((x0+h/2.0),(y0+m2*h/2.0));
        m4=f((x0+h),(y0+m3*h));
        m=((m1+2*m2+2*m3+m4)/6);
        y=y+m*h;
        x=x+h;
        printf("%f\t%f\n",x,y);
    }
}
float f(float x,float y)
{
    float m;
    m=(x-y)/(x+y);
    return m;
} "