利用向前Euler尤拉近似法 解一階常微分方程ODE
y' = -y + t +1 , 0<= t <= 1 , y(0)=1 , h=0.2
真實解= e^(-t) + t
Ｃ語言程式:
/* ex5-1.c Forward Euler Method is used for
* solving y'=f(y,t) of first order
* ordinary differential equation
* with initial condition y(0)=y0
* known.
*/
#include <stdio.h>
#include <math.h>
#define F(y,t) (-y+t+1) //y' = -y + t +1
#define w(t) (exp(-t)+t) //真實解
void main()
{
int i,n=5;
double h=0.2,y,t,y0=1,t0=0;
y=y0;
t=t0;
printf("t y(t) w(t) error\n");
printf("========================================\n");
printf("%.2lf %10.6lf %10.6lf %10.6lf\n",
t,y,w(t),fabs(y-w(t)));
for(i=1;i<=n;i++)
{
y=y+h*F(y,t);
t=t+h;
//if(i%5==0)
printf("%.2lf %10.6lf %10.6lf %10.6lf\n",
t,y,w(t),fabs(y-w(t)));
}
return;
}
t y(t) w(t) error
========================================
0.00 1.000000 1.000000 0.000000
0.20 1.000000 1.018731 0.018731
0.40 1.040000 1.070320 0.030320
0.60 1.112000 1.148812 0.036812
0.80 1.209600 1.249329 0.039729
1.00 1.327680 1.367879 0.040199
...Program finished with exit code 41
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