取 h=0.01 , 0.001 , 0.0001
/* ex5-2.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+2*exp(4*t))
#define w(t) ((2.0/3.0)*exp(4.0*t)-(11.0/3)*exp(t))
void main()
{
int i,n=10000;
double h=0.0001,y,t,y0=-3,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%1000==0)
printf("%.2lf %10.6lf %10.6lf %10.6lf\n",
t,y,w(t),fabs(y-w(t)));
}
return;
}
修改的地方
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int i,n=100;
double h=0.01,y,t,y0=-3,t0=0;
if(i%10==0)
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/* ex5-2.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+2*exp(4*t))
#define w(t) ((2.0/3.0)*exp(4.0*t)-(11.0/3)*exp(t))
void main()
{
int i,n=100;
double h=0.01,y,t,y0=-3,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%10==0)
printf("%.2lf %10.6lf %10.6lf %10.6lf\n",
t,y,w(t),fabs(y-w(t)));
}
return;
}
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int i,n=1000;
double h=0.001,y,t,y0=-3,t0=0;
if(i%100==0)
1.00 26.423010 26.431733 0.008724
t y(t) w(t) error
========================================
0.00 -3.000000 -3.000000 0.000000
0.10 -3.057792 -3.057744 0.000048
0.20 -2.994917 -2.994783 0.000134
0.30 -2.736347 -2.736071 0.000276
0.40 -2.168508 -2.168002 0.000506
0.50 -1.120143 -1.119274 0.000869
0.60 0.666247 0.667682 0.001435
0.70 3.577031 3.579338 0.002307
0.80 8.191065 8.194703 0.003639
0.90 15.374616 15.380278 0.005663
1.00 26.423010 26.431733 0.008724
...Program finished with exit code 41
Press ENTER to exit console.
t y(t) w(t) error
========================================
0.00 -3.000000 -3.000000 0.000000
0.10 -3.062524 -3.057744 0.004780
0.20 -3.007973 -2.994783 0.013190
0.30 -2.763301 -2.736071 0.027230
0.40 -2.217918 -2.168002 0.049915
0.50 -1.205054 -1.119274 0.085780
0.60 0.526053 0.667682 0.141629
0.70 3.351680 3.579338 0.227657
0.80 7.835576 8.194703 0.359127
0.90 14.821414 15.380278 0.558865
1.00 25.570747 26.431733 0.860987
t y(t) w(t) error
========================================
0.00 -3.000000 -3.000000 0.000000
0.10 -3.058228 -3.057744 0.000484
0.20 -2.996118 -2.994783 0.001335
0.30 -2.738828 -2.736071 0.002757
0.40 -2.173055 -2.168002 0.005052
0.50 -1.127956 -1.119274 0.008682
0.60 0.653348 0.667682 0.014334
0.70 3.556298 3.579338 0.023040
0.80 8.158359 8.194703 0.036344
0.90 15.323721 15.380278 0.056557
1.00 26.344602 26.431733 0.087131
...Program finished with exit code 41
Press ENTER to exit console.
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