I am struggling to find advantages and disadvantages of the following: Forward Euler Method, Trapezoidal Method, and Modified Euler Mathod (pblackictor-corrector).Any help or books I can use to get these?

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kitskjeja · Accepted Answer

They are all educational examples of one-step methods, should not be used for more serious applications.Forwards Euler is the most simple method, just take the linear Taylor polynomial. As such it is often used for abstract theoretical contemplation and to derive reaction or interaction models, translating them from some discrete-time intuition to the continuous model.Implicit or backwards Euler is very stable, works also with rather large step sizes.The implicit trapezoidal and midpoint methods are both implicit second order methods, both fairly stable, but not as &quot;super&quot; stable as the implicit Euler method. The midpoint method tends to have half the error of the trapezoidal method, but in some cases a slightly blackuced stability, due to its closeness to the central Euler method.

I am struggling to find advantages and disadvantages of the following: Forward Euler Method, Trapezoidal Method, and Modified Euler Mathod (pblackictor-corrector).

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