euler approximation method source code

This snippet submitted by eric mbakop on 2005-04-16. It has been viewed 46831 times.
Rating of 5.6 with 329 votes
 
 #include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
void menu(double **coefficient,int n,double ct,double xo,double yo,double h,double a,
double b);

void compute_approximation_euler1(double **coefficient,int n,double ct,double xo,
double yo,double h, double a,double b);

double f(double **coefficient,int n,double ct,double x,double y);

int main(){
    double *coefficient[2];
    double ct,xo,yo,a,b,h;
    int n,i;
    
    printf("what's the highest degree of f(x,y)?\t");
    fflush(stdin);
    scanf("%d",&n);
    n=n+1;
    for(i=0;i<2;i++){
    coefficient[i]=(double *)calloc(n,sizeof (double));
}
    for(i=1;i<n;i++){
    printf("what's the coefficient of x to the %d power\t",i);
    fflush(stdin);
    scanf("%lf",&coefficient[0][i]);
}

   for(i=1;i<n;i++){
    printf("what's the coefficient of y to the %d power\t",i);
    fflush(stdin);
    scanf("%lf",&coefficient[0][i]);
} 
    printf("what's the constant term?\t");
    fflush(stdin);
    scanf("%lf",&ct);
    
    printf("what's x initial\t");
    fflush(stdin);
    scanf("%lf",&xo);
    
     printf("what's y initial\t");
    fflush(stdin);
    scanf("%lf",&yo);
    
    printf("what's the stepsize\t");
    fflush(stdin);
    scanf("%lf",&h);
    
    printf("over what interval do you want to approximate f(x)->( a b)\t");
    fflush(stdin);
    scanf("%lf%lf",&a,&b);
    menu(coefficient,n,ct,xo,yo,h,a,b);
    system("pause");
    free(coefficient);
    
}

  void menu(double **coefficient,int n,double ct,double xo,double yo,double h,double a,
double b){
       int k;
       system("cls");
       printf("choose the method that you want to use for the approximation\n");
       printf("1.first order euler method\n");
       fflush(stdin);
       scanf("%d",&k);
       
       switch(k){
                 
       case 1:
           compute_approximation_euler1(coefficient,n,ct,xo,yo,h,a,b);
            break;
       default:
               printf("you did not enter a valid number\n");
               }
               }
 void compute_approximation_euler1(double **coefficient,int n,double ct,double xo,
double yo,double h, double a,double b){
       
       FILE *file;
       int k,i;
       double *x;
       double *y;
       
       system("cls");
       file=fopen("c:\\approximation_euler1.dat","w");
       
       if (file==NULL){
       printf("the file cannot be created");
       system("pause");
       }
       
       else
       
       k=(int)((b-a)/h)+1;
       x=(double *)calloc(k,sizeof (double));
       y=(double *)calloc(k,sizeof (double));
       x[0]=xo;
       y[0]=yo;
       
       for(i=0;i<k;i++){
       
       x[i+1]=x[i]+h;
       y[i+1]=y[i]+h*f(coefficient,n,ct,x[i],y[i]);
       fprintf(file,"4.2%lf\t4.2%lf\n",x[i],y[i]);
       }
       free(x);
       free(y);
       fclose(file);
       printf("to view the results open the file approximation_euler1");
       system("pause");
       exit(1);
       }
       
double f(double **coefficient,int n,double ct,double x,double y){
       int k;
       double sum,xsum,ysum;
                        
       for(k=1;k<n;k++){
       
       xsum=xsum+x*pow(coefficient[0][k],k);
       }
       
       for(k=1;k<n;k++){
       
       ysum=ysum+y*pow(coefficient[1][k],k);
       }    
       sum=xsum+ysum+ct;
       
       return(sum);

}
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