Given the problem:
$y′ = (t − 1)\sin(y),\;\;\;y(1) = 1$ find an approximation for $y(2)$.
Give an upper bound for the global error taking $n = 4$ (i.e., $h = \frac{1}{4}$)
The goal is to find an upper bound, not actually find an approximation for $y(2)$.
However I don't think it is possible to find an upper bound as we need to use the equation
$|E_n| \leq \frac{T}{L}[(e^{(t_n - t_0)L} - 1)]$
where $T$ is the max truncation error and $L$ is the Lipschitz constant.
But I am unable to get a Lipschitz constant from $y′ = (t − 1)\sin(y)$, I don't think it's possible without being given a bound on $t$.
$|f(t, u) - f(t,v)| = |(t-1)\sin(u) - (t-1)\sin(v)|= |t-1||\sin(u) - \sin(v)|$
$\sin\;$ has Lipschitz constant of $2$ so we can say
$\leq 2|t-1||u - v|$
And where can I go from here...?
Is the question just not well defined or am I missing something?