列主元高斯消元法.cpp

列主元高斯消元法已通过上机验证适合于数值计算学习者编程欢迎下载

#include<stdio.h>
#include<math.h>
#define  f(x,y)  -(x*x*y*y)//导数
#define  y(x)    2.0/(1.0+x*x*x)//准确解
void main()
{
	int i,j;
	long double h[4]={0.1,0.05,0.025,0.0125};//步长
	int m[4]={15,30,60,120};//不同步长时迭代到1.5的循环次数
	long double x0,y0,xn,yn,yn1,yn2;
	long double k1,k2,k3,k4;
	yn2=(long double)y(1.5);//计算准确值
	x0=0.0;y0=3.0;
    printf("h        数值结果y(1.5)          精确解           数值误差  \n");
	for(i=0;i<4;i++)
	{   xn=x0;yn=y0;//初始化
		for(j=0;j<m[i];j++)
		{
			k1=f(xn,yn);
			k2=f((xn+h[i]/2.0),(yn+h[i]*k1/2.0));
			k3=f((xn+h[i]/2.0),(yn+h[i]*k2/2.0));
			k4=f((xn+h[i]),(yn+h[i]*k3));
			yn1=yn+h[i]/6.0*(k1+2*k2+2*k3+k4);//龙格-库塔四阶公式
			xn=xn+h[i];
			yn=yn1;
		}
			printf("%.12lf       %.12lf         %.12lf          %.12lf    \n",h[i],yn1,yn2,fabs(yn2-yn1));//输出
	}
}