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> The Euler method is too inaccurate to be useful.

You can make it as accurate as you want by shrinking the time step. :)




That's no way to go through life.


This is actually not true since rounding errors will compound.


Sure, in IEEE 754! But to call the various explicit variants of Euler useless is a bit off. Symplectic Euler is quite nice in certain applications. Hell, Newton derived a number of theorems by reasoning about explicit Euler discretizations (usually geometrically).




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