euler.c

【欧拉算法】 微分方程的本质特征是方程中含有导数项,数值解法的第一步就是...欧拉(Euler)算法是数值求解中最基本、最简单的方法,但其求解精度较低,一般不在...对于常微分方程: dy/dx=f(

#include "stdio.h"
#include "math.h"
#define N 100
main()
{
    int n,i;
    double x[N],y[N],ey[N],wc[N],a,b,h;
    
    printf("/*************************************\\\n");
    printf("       Use eular solove question!\n");
    printf("input y(1)=");
    scanf("%lf",&y[0]);
    printf("\ninput the rang a,b:");
    scanf("%lf,%lf",&a,&b);
    x[0]=a;
	ey[0]=y[0];
	wc[0]=y[0]-ey[0];
    printf("\ninput n(n<=N)=");
    scanf("%d",&n);
    h=(b-a)/n;
    for(i=1;i<n+1;i++)
		x[i]=x[0]+i*h;
    for(i=1;i<n+1;i++)
	{
    ey[i]=ey[i-1]+h*(0-(4*ey[i-1])/x[i-1]-2/(x[i-1]*x[i-1])-ey[i-1]*ey[i-1]);
	y[i]=(1-x[i])/(x[i]*x[i]-x[i]/2);
	wc[i]=y[i]-ey[i];
	}
	printf("/*************************************\\\n");
	printf("x[i]     Eular answer   sure answer      误差\n");
    for(i=0;i<n+1;i++)
    {
		printf("%lf   ",x[i]);
    	printf("%lf      ",ey[i]);
	    printf("%lf    ",y[i]);
	    printf("%lf",wc[i]);
    	printf("\n");
    }
}