I am beginner in c++ and I need your help plz. I implemented euler method for solving simple ODEs (y' = x -y, y(0)=1)and it is forward in time(from t=0 to t=1) and it worked well, my question is : I want to run this code backward in time(i.e. from t=1 to t=0) what i have to change in my code?
Code:
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/* Euler for a set of first order differential equations */
#include <stdio.h>
#include <math.h>
#define dist 0.2 /* stepsize in t*/
#define MAX 1.0 /* max for t */
int N=1;
void euler(double x, double y[], double step); /* Euler function */
double f(double x, double y[], int i); /* function for derivatives */
main()
{
double t, y[N];
int j;
y[0]=1.0; /* initial condition */
for (j=0; j*dist<=MAX ;j++) /* time loop */
{
t=j*dist;
printf("j = %d,t = %f y[0] = %f\n", j,t, y[0]);
euler(t, y, dist);
}
}
void euler(double x, double y[], double step)
{
double s[N]; /* for euler */
int i;
{
for (i=0;i<N;i++)
{ s[i]=step*f(x, y, i);
}
}
{
for (i=0;i<N;i++)
y[i]+=s[i];
}
}
double f(double x, double y[], int i)
{
if (i==0) return(x-y[0]); /* derivative of first equation */
}
many thanks in advance!