Euler’s Method 란 무엇인가?
Analytic 한 풀이
y’ = f(x,y) , y(x0)=y0
L(x) = y0 + f(x0,y0)(x-x0)
We now let ‘h’ be a positive increment of the x- axis, as shown in this figure.
Then by replacing x by x1=x0+h, we get
L(x1) = y0 + f(x0,y0)(x0+h-x0) or
y1 = y0 + hf(x1,y1) , where y1 = L(x1)
the point tangent line is an approximation to the point (x1,y(x1)) on the solution curve.
Continuing in this manner,
yn+1 = yn + hf(xn, yn) where xn=x0+nh (n=0,1,2,…..)
This procedure of using successive “tangent lines” is called Euler’s Method.