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Euler's Method

The simplest method of solving ODE's is Euler's method:

yn+1 = yn + hf(yn).


In order to integrate from the initial data at t = 0 up to t = T, divide the interval into N equal steps of size h = T/N and approximate y(tn = nh) = yn. This method works and is sometimes used in practice, but much better alternatives are described below. Nonetheless, it is the conceptual basis of all other methods, and a little analysis gives insight into how they all work.


G. Bard Ermentrout