# Euler Method¶

For linear first ODE,

$\frac{dy}{dx} = f(x, y),$

we can discretize the equation using a step size $$\delta x \cdot$$ so that the differential equation becomes

$\frac{y_{n+1} - y_n }{ \delta x } = f(x_n, y_n),$

which is also written as

(1)$y_{n+1} = y_n + \delta x \cdot f(x_n, y_n).$

This is also called forward Euler differencing. It is first order accurate in $$\Delta t$$.

Generally speaking, a simple iteraction will do the work.

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