# euler approximation method source code

This snippet submitted by eric mbakop on 2005-04-16. It has been viewed 44312 times.
Rating of 5.4 with 281 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);
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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