Ordinary differential equations the Euler method

6 Ordinary differential equations the Euler method Quite commonly, differential equations appear in the form 

The Euler method has little practical value, but forms the basis for most of the more elaborate methods. It consists in a first-order expansion of the derivative. The approximation at step t n+l) is 

This equation has an exact solution y=exp(—t2). For a rather coarse time step of 0.1, we obtain 

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