alg051.c

Numerical Anaysis 8th Edition Burden and Faires

/*
*    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.
*/

#include<stdio.h>
#include<math.h>
#define true 1
#define false 0

main()
{
   double A,B,ALPHA,H,T,W;
   int I,N,OK;
   FILE *OUP[1];

   double F(double, double);
   void INPUT(int *, double *, double *, double *, int *);
   void OUTPUT(FILE **);

   INPUT(&OK, &A, &B, &ALPHA, &N);
   if (OK) {
      OUTPUT(OUP);
      /* STEP 1 */
      H = (B - A) / N;
      T = A;
      W = ALPHA;
      fprintf(*OUP, "%5.3f %11.7f\n", T, W);
      /* 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 */
         fprintf(*OUP, "%5.3f %11.7f\n", T, W);
      }
      /* STEP 5 */
      fclose(*OUP);
   }
   return 0;
}
/*  Change function F for a new problem   */
double F(double T, double Y)
{
   double f; 

   f = Y - T*T + 1.0;
   return f;
}

void INPUT(int *OK, double *A, double *B, double *ALPHA, int *N)
{
   double X; 
   char AA;

   printf("This is Eulers Method.\n");
   printf("Has the function F been defined?\n");
   printf("Enter Y or N.\n");
   scanf("%c",&AA);
   *OK = false;
   if ((AA == 'Y') || (AA == 'y')) {
      *OK = false;
      while (!(*OK)) {
         printf("Input left and right endpoints separated by blank\n");
         scanf("%lf %lf", A, B);
         if (*A >= *B) 
            printf("Left endpoint must be less than right endpoint\n");
         else *OK = true;
      }
      printf("Input the initial condition\n");
      scanf("%lf", ALPHA);
      *OK = false;
      while(!(*OK)) {
         printf("Input a positive integer for the number of subintervals\n");
         scanf("%d", N);
         if (*N <= 0.0) printf("Number must be a positive integer\n");
         else *OK = true;
      }
   }
   else 
      printf("The program will end so that the function can be created.\n");
}

void OUTPUT(FILE **OUP)
{
   char NAME[30];
   int FLAG; 

   printf("Choice of output method:\n");
   printf("1. Output to screen\n");
   printf("2. Output to text file\n");
   printf("Please enter 1 or 2\n");
   scanf("%d", &FLAG);
   if (FLAG == 2) {
      printf("Input the file name in the form - drive:name.ext\n");
      printf("For example   A:OUTPUT.DTA\n");
      scanf("%s", NAME);
      *OUP = fopen(NAME, "w");
   }
   else *OUP = stdout;
   fprintf(*OUP, "EULERS METHOD\n\n");
   fprintf(*OUP, "    t           w\n\n");
}