2.5.1 Euler 法

euler.c

/* euler.c */

#include <stdio.h>
#include <math.h>

int main()
{
    int i, N;
    double a = 0.0, b = 1.0;
    double x0;
    double t, x, h;
    double f(double, double);

    printf(" x0="); scanf("%lf", &x0);
    printf(" N="); scanf("%d", &N);

    h = (b - a) / N;

    t = a; x = x0;
    printf("%g %g\n", t, x);

    for (i = 0; i < N; i++) {
        x = x + h * f(t,x);
        t = t + h;
        printf("%g %g\n", t, x);
    }
    printf("%g %20.15e\n", t, x);
    return 0;
}

double f(double t, double x)
{
    return x;
}

実行結果

mathpc00% ./euler
 x0=1
 N=100
0 1
0.01 1.01
0.02 1.0201
0.03 1.0303
0.04 1.0406
0.05 1.05101
0.06 1.06152
0.07 1.07214
0.08 1.08286
0.09 1.09369
中略
0.91 2.47312
0.92 2.49785
0.93 2.52283
0.94 2.54806
0.95 2.57354
0.96 2.59927
0.97 2.62527
0.98 2.65152
0.99 2.67803
1 2.70481
1 2.704813829421526e+00
mathpc00%