# Math Help - Euler Approximation

1. ## Euler Approximation

Use Euler’s method to estimate y (1.2), the solution to the IVP (initial value problem)

y' = 2t - y, y (1) = -1, and step size h = 0.1.

2. Originally Posted by Oblivionwarrior
Use Euler’s method to estimate y (1.2), the solution to the IVP (initial value problem)

y' = 2t - y, y (1) = -1, and step size h = 0.1.
Where is the trouble?

The approximate solution to the initial value problem

$\frac{dy}{dt} = f(t, y)$ where $y(t_0) = y_0$

is given by $y_{n+1} = y_n + h f(t_n, y_n)$.

$y(1.1) = y_1 = y_0 + h (2 t_0 - y_0) = -1 + (0.1) (2 - -1) = -1 + 0.3 = -0.7$.
$y(1.2) = y_2 = y_1 + h (2 t_1 - y_1) = -0.7 + (0.1) (2.2 - -0.7) = -0.7 + 0.29 = -0.41$.