How Does Euler's Method Solve Differential Equations?

[squenshl]

Homework Statement

Consider the initial value problem y' = f(t,y), y(t₀) = y₀
where f: R x R \rightarrow R. An approximate solution to the problem can be found using Euler's method. This generates the approximation y_i to f(t_i) at t_i = t₀ + ih, i = 1,2,..., using the formula y_i = y_i-1 + hf(t_i-1,y_i-1). Implement Euler's method and then show that your implementation is correct.

Homework Equations

Eulers method equation.

The Attempt at a Solution

I am not sure exactly what it is asking. Is it asking for a numerical example or what?

 

[LCKurtz]

If this is from a class, ask your teacher what it intended. As the problem is worded I might try something like

y' = x - y, y(0) = 1

and solve it with Euler's method and compare it with the actual solution. But I would ask.