////////////////////////////////////////////////////
//注釋請參看Euler法程序 Euler.cpp

////////////////////////////////////////////////////
//	程序4.2 — 改進的歐拉方法

#include <stdlib.h>
#include <stdio.h>
#include <conio.h>
#include <string.h>
//#include <graphics.h>
#include <math.h>

#include "expressi.cpp"

void Improved_Euler(char FxyString[],float x0,float y0,float h,int n)
{
	int i;
	float yi,tmp;

	if(CreateFxy(FxyString)) return;

	yi = y0;
	for(i=1;i<n;++i)
	{
		tmp = yi;
		
		yi = yi+h*f(x0+(i-1)*h,yi);//Euler公式

		yi = tmp+h/2*(f(x0+(i-1)*h,tmp)+f(x0+i*h,yi)); //梯型公式
		
		printf("\ny%d=%f",i,yi);
	}

}

void main()
{
	float x0,y0,h;
	int n;
	char FxyString[200];

	printf("\nInput function,x0,y0,h,n: ");
	scanf("%s %f %f %f %d",FxyString,&x0,&y0,&h,&n);

	Improved_Euler(FxyString,x0,y0,h,n);

	getch();
}

/*
	運行實例

Input function,x0,y0,h,n: y-2*x/y 0 1 0.1 11

y1=1.095909
y2=1.184097
y3=1.266201
y4=1.343360
y5=1.416402
y6=1.485956
y7=1.552514
y8=1.616475
y9=1.678167
y10=1.737868
*/