4.1欧拉公式 Chapter 4 Initial -value problems for ODE y 狄思想:用向前差商近似代替微商 y(Xo=yo y(x)≈yXn+)y(x) h=Xn+iXn f(xny×n) yxn+,) yX1=yx)+hf(x) yn1=yn+hf(xnyn)—欧拉公式( Euler scheme) Jx%)= n=01,2 Yn+1=y, +hf(xn,y, HUST!思想:用向前差商近似代替微商. ≈ n+1 n n n+1 n y(x )-y(x ) y'(x ) h=x -x h  ⋅⋅⋅⋅⋅⋅  0 0 n+1 n n n y(x )=y n=0,1,2, y =y +hf(x ,y ) ——欧拉公式 Euler Scheme 4.1 欧拉公式 ∴ ≈ n+1 n n n y(x )- y(x y(x ) f( , x) . ) h ( ) ( )  ' 0 0 y = f x,y y x =y ∴ ≈ n+1 n n n y(x ) y(x )+hf(x ,y(x )) ∴ n+1=y +hf(x ,y n n n y )