MAT244-2013F > MidTerm

MT, P5


Victor Ivrii:
Apply the Euler method with step $h=\frac{1}{3}$ to the initial value problem
y'=3y^2-t;\quad y(0)=0
to find approximate values of $y(\frac{1}{3}), y(\frac{2}{3})$ and $y(1)$.

Xuewen Yang:
see attach

Xiaozeng Yu:

Huan Ying Huang:
$$y_n=y_{n-1}+h f(t_n,y_n),$$
with $f(t,y)=3y^2-t$.

$t_0=0$, $y_0=0$,  $f(t_0,y_0)=0$,

$y_1=0+\frac{1}{3}\cdot 0=0$.

$t_1=\frac{1}{3}$,   $y_1=0$,  $f(t_1,y_1)=-\frac{1}{3}$,

$y_2= 0+ \frac{1}{3}\cdot (-\frac{1}{3})=-\frac{1}{9}$,

$t_2=\frac{2}{3}$,   $y_2=-\frac{1}{9}$,  $f(t_2,y_2)=-\frac{17}{27}$,

$y_3=-\frac{1}{9}+\frac{1}{3}\cdot (-\frac{17}{27}) =-\frac{26}{81}$.

I edited this post. Do not use "x" or "*" for multiplication (* is a convolution, to be studied in APM346 f.e.)  V.I.


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