(*  EULER'S ALGORITHM 5.1
*
*   To approximate the solution of the initial value problem:
*    Y' = F(T,Y), A <= T <= B, Y(A) = ALPHA,
*    at n+1 equally spaced points in the interval [A,B].
*
*   INPUT: endpoints a, b; initial condition ALPHA; integer n.
*
*  OUTPUT: Approximation W to Y at the (n+1) values of T.
*)
TEMP = Input["This is Euler's Method\n
 Input the function F(T,Y) in terms of t and y\n 
 \n
 For example: y-t^2+1\n"];
F[t_,y_] :=Evaluate[TEMP];
OK = 0;
While[OK == 0,
   A = Input["Input the left endpoint\n"];
   B = Input["Input the right endpoint\n"];
   If[A >= B,
      Input["Left endpoint must be less than right endpoint\n
      \n
      Press 1 [enter] to continue\n"],
      OK = 1;
   ];
];
ALPHA = Input["Input thr initial condition\n"];
OK = 0;
While[OK == 0,
   n = Input["Input a positive integer for the number of\n
   subintervals\n"];
   If[n <= 0,
      Input["Number must be a positive integer\n
	\n
      Press 1 [enter] to continue\n"],
      OK = 1;
   ];
];
If[OK == 1,
   FLAG = Input["Select output destination\n
                 1. Screen\n
                 2. Text file\n
                 Enter 1 or 2\n"];
   If[FLAG == 2,
      NAME = InputString["Input the file name\n
                          For example:   output.dta\n"];
      OUP = OpenWrite[NAME,FormatType->OutputForm],
      OUP = "stdout";
   ];
   Write[OUP,"Euler's Method\n"];
   Write[OUP,"t          w  \n"];
   Write[OUP,"\n"];
   (* Step 1 *)
   H = N[(B-A)/n];
   T = A;
   W = ALPHA;
   Write[OUP,SetPrecision[T,9],"        \n",SetPrecision[W,9]];
   (* Step 2 *)
   For[i = 1,
      i <= n,
      i++,
      (* Step 3 - Compute W(I) *)
      W = W+H*F[T,W];
      (* Compute T(I) *)
      T = A+i*H;
      (* Step 4 *)
      Write[OUP,SetPrecision[T,9],"        \n",SetPrecision[W,9]];
   ];
   (* Step 5 *)
   If[OUP == "OutputStream[",NAME," 3]",
      Print["Output file: ",NAME," created successfully\n"];
      Close[OUP]
   ];
];
Quit[];