//  Marc Courtright 9/15/02
// numerical_int.sce
// a program that uses numerical integration to approximate the area under a function
// To run this in Scilab use 'File' then 'Exec'.

// global variables

M=1;					// mass
h=2;					// step
start_time=0;				// lower limit
total_time=100;				// upper limit




function[F,vprime,v]=v(M,h,t)
if(0<=t<=4) then, F=1,else,F=2,end	// set up the step input of F
vprime=F/M;				// d/dt (function)
v=V((i-1),5)+h*vprime;			// f(t+h)=f(t)+h*fprime
endfunction

// declarations and initialization

imax=((total_time-start_time)/h)		// stopping point for loop index "i"
n=imax+1

	// initial conditions

Vmatrix = matrix(v,n,5);				// matrix to store v and vprime
V(1,:)=["i  ","t  ","F(N) ","d/dt v ","v  "];	// header for the matrix
V(2,:)=[0,0,0,0,0]				//initial conditions

// calculations

for i=1:imax,
	t=h*i;
	V(i,1)=i
	V(i,2)=t
	V(i,3:5)=v(M,h,t)
	i=i+1;
end;

// write to file

unix("del c:\temp\numerical_int.text");
write("c:\temp\numerical_int.text", [Vmatrix]);