#include<iostream>

 #include<cmath>

 #include<cstdio>

 #include<iomanip>

 using namespace std;

 double h=0.1;//步差

 double xi[]={};

 double ol_yi[]={};

 double gol_yi[]={};

 double rk_yi[]={};

 double real_yi[]={};

 double f(double x,double y){

     return *x/(*y*y);

 }//f(x,y)

 void OLFunction(){

     for(int i=;i<;i++){

         ol_yi[i+]=ol_yi[i]+h*f(xi[i],ol_yi[i]);

     }

 }//欧拉方法

 void GOLFunction(){

     for(int i=;i<;i++){

         gol_yi[i+]=gol_yi[i]+

             h*(

                 f(xi[i],gol_yi[i])

                 +f(xi[i+],gol_yi[i]+h*f(xi[i],gol_yi[i]))

             )/;

     }

 }//改进欧拉方法

 void RKFunction(){

     double K1,K2,K3,K4;

     for(int i=;i<;i++){

         K1=f(xi[i],rk_yi[i]);

         K2=f(xi[i]+h/,rk_yi[i]+h*K1/);

         K3=f(xi[i]+h/,rk_yi[i]+h*K2/);

         K4=f(xi[i]+h,rk_yi[i]+h*K3);

         rk_yi[i+]=rk_yi[i]+h*(K1+*K2+*K3+K4)/;

     }

 }//经典龙格贝法

 void RFunction(){

     for(int i=;i<;i++){

         real_yi[i]=pow(1.0+xi[i]*xi[i],/3.0);

     }

 }//真实解

 int main(){

     int i;

     for(i=;i<;i++){

         xi[i]=xi[i-]+h;

     }//求xi[]

     OLFunction();//四种计算方法

     GOLFunction();

     RKFunction();

     RFunction();

     printf("-------------------------------------------------\n");

     printf("xi  | 欧拉     | 改进欧拉 | 经典R-K  | 准确解 \n");

     printf("-------------------------------------------------\n");

     for(i=;i<;i++){

         printf("%.1lf | %.6lf | %.6lf | %.6lf | %.8lf\n",

             xi[i],ol_yi[i],gol_yi[i],rk_yi[i],real_yi[i]);

     }

     getchar();

     return ;

 }