-Letís consider the initial-value problem
Dy/dt = 2-y, y(0)=1
How can I compute three different approximate solutions corresponding, for an example, to Δt= 1.0, 0.5 and 0.25 over the interval 0 ≤ t ≤ 4 by using Eulerís method. Also how can I graph all three solutions? What predictions can I make about the actual solutions to the initial-value problem? How can I include a table of the approximate values of the dependent variable?
I know we want to start first by approximating the solution of the initial value problem y'(t)=f(t,y(t)), y(t0)=y0. Is Euler method yn+1=yn+hf(tn,yn)? I know we must first compute f(t0,y0). Because this differential equation depends only on y, so we need only worry about inputting the values for y. After that I get stuck? Or am I right at all?