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Explain the Euler method for solving an ODE

The Euler method

It steps a solution forward using the slope at the current point. Given the rate of change, the next value is:

yn+1 = yn + h · f(tn, yn)

Here h is the step size. Smaller h means less error. In code:

Set t₀, y₀, h
yₙ₊₁ = yₙ + h·f(tₙ,yₙ)
Repeat to t_end
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