euler.h

欧拉算法的改进

double f(double x,double y){
return y-2*x/y;}
double improved_euler(double x,double y,double h,int n){
int i;
double yi,tmp;
yi=y;
for(i=1;i<=n;i++)
{
tmp=yi;
yi=yi+h*f(x+(i-1)*h,yi);
yi=tmp+h/2*(f(x+(i-1)*h,tmp)+f(x+i*h,yi));
printf("\ny%d=%f",i,yi);
}
} 
double longgekuta(double a, double b,double h,int n)
{
int i;
double xs,k[5];
double x[20];
double y[20];
x[0]=a;
xs=x[0]+n*h;
y[0]=b;
	 for(i=0;i<n;i++)
  {
   x[i+1]=x[i]+h;
   k[1]=f(x[i],y[i]);
   k[2]=f(x[i]+h/2,y[i]+h*k[1]/2);
   k[3]=f(x[i]+h/2,y[i]+h*k[2]/2);
   k[4]=f(x[i]+h,y[i]+h*k[3]);
   y[i+1]=y[i]+h*(k[1]+2*k[2]+2*k[3]+k[4])/6;
   printf("\nd%d=%f",i+1,y[i+1]);
  if(x[i+1]>=xs) return (0);
  }
return(0);
}