Approximating $y'(t^n)$ at the relation $y'(t^n)=f(t^n,y(t^n))$ with the difference quotient $\left[\frac{y(t^{n+1})-y(t^n)}{h} \right]$ we get to the Euler method. Approximating the same derivative with the quotient $\left[\frac{y(t^{n})-y(t^{n-1})}{h} \right]$ we get to the backward Euler meth...

Whether or not a question is homework or not, is not a major concern of mine. It is typically quite difficult to determine, and in those cases where it is more or less obvious the question is normally lacking for other reasons, too (see below). What is a concern of mine is the quality of questio...

If one screen costs 200.00 and every day you make 2.00 from one screen. How many days until you have 100 screens if you buy a screen every time you get 200.00?

I am looking at the following exercise: Consider the initial value problem $\left\{\begin{matrix} x''(t)=x(t)\\ x(0)=a\\ x'(0)=b \end{matrix}\right.$ Write it as a system of First-Order ODES with suitable initial values and show that Euler method can get unstable for a great step $(h)$. Tha...