# To evaluate ordinary differential equations by RK-4 (Classical) Method

Evaluating ordinary differential equations by RK-4 or classical method both order first and second
//To compute ordinary differential equations by RK-4 or classical method for order first
#include
#include
#include
void main()
{
cout<<“\t first order R-K 4th Classical Method\t”<
double h,n,m1,i,m2,m3,m4,x,y;
cout<<“Number of intervals “;
cin>>n;
cout<
cout<<“Enter the value of h”<<<“h = “;
cin>>h;
cout<<“Enter the value of x0″<<<“x0 = “;
cin>>x;
cout<<“Enter the value of y0″<<<“y0 = “;
cin>>y;
cout<
for(i=0;i<=n;i++)
{
x[i+1]=x[i]+h;
m1=h*.5*(1+x[i])*(y[i]*y[i]);
m2=h*.5*(1+(x[i]+.5*h))*(y[i]+m1*.5*h)*(y[i]+m1*.5*h);
m3=h*.5*(1+(x[i]+.5*h))*(y[i]+m2*.5*h)*(y[i]+m2*.5*h);
m4=h*.5*(1+(x[i]+h))*(y[i]+m3*h)*(y[i]+m3*h);
y[i+1]=y[i]+(m1+2.0*m2+2.0*m3+m4)/6;
cout<<“x”<<<“= “<<
cout<<“y”<<<“= “<<
cout<
}
getch();
}
// To compute ordinary differential equations by RK-4 or classical method for order second
#include
#include
#include
void main()
{
cout<<“\t 2nd order order R-K 4th Order Method\t”<
double h,n,m1,i,m2,m3,m4,p1,p2,p3,p4,x,y,z;
cout<<“Number of intervals “;
cin>>n;
cout<
cout<<“Enter the value of h”<<<“h = “;
cin>>h;
cout<<“Enter the value of x0″<<<“x0 = “;
cin>>x;
cout<<“Enter the value of y0″<<<“y0 = “;
cin>>y;
cout<<“Enter the value of z0″<<<“z0 = “;
cin>>z;
cout<
for(i=0;i<=n;i++)
{
x[i+1]=x[i]+h;
m1=h*z[i];
p1=h*(6*x[i]+3*y[i]-2*z[i]);
m2=h*(z[i]+.5*p1);
p2=h*(6*(x[i]+.5*h)+3*(y[i]+m1*.5)-2*(z[i]+.5*p1)) ;
m3=h*(z[i]+.5*p2);
p3=h*(6*(x[i]+.5*h)+3*(y[i]+m2*.5)-2*(z[i]+.5*p2)) ;
m4=h*(z[i]+.5*p3);
p4=h*(6*(x[i]+.5*h)+3*(y[i]+m3*.5)-2*(z[i]+.5*p3)) ;
y[i+1]=y[i]+(m1+2.0*m2+2.0*m3+m4)/6;
z[i+1]=z[i]+(p1+2.0*p2+2.0*p3+p4)/6;
cout<<“x”<<<“= “<<
cout<<“y”<<<“= “<<
cout<<“z”<<<“= “<<
cout<
}
getch();
}
To evaluate ordinary differential equations by RK-4 (Classical) Method in C++ Programming Language for Numerical Methods for Engineering Students