[算法] [常微分方程] [欧拉法 改进欧拉法 经典R-K算法]

 #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 ;
 }