Difference Between Euler and Forward (Explicit) Euler

Jacob Roman · 2006-03-01T17:43:18

Not sure if it's the same thing or not but are there differences between the two?

Math and Physics Programming

Started by Jacob Roman February 28, 2006 08:37 AM

11 comments, last by jjd 18 years, 1 month ago

someusername

427

March 01, 2006 05:34 PM

So, within a loop, integrating acceleration to find position, the two methods would look like:

a)forward (explicit) euler

1.vel = v02.pos = p03.loop{4.  pos += vel*dt;5.  Calculate acceleration6.  vel += acc*dt;7.}

while the other
b) backward (implicit)

1.vel = v02.pos = p03.loop{4.  Calculate acceleration5.  vel += acc*dt6.  pos += vel*dt7.

right?

I've seen both implementations, but I didn't realize they were given different names...
They are different, indeed.

Sneftel

1,788

March 01, 2006 05:38 PM

The second one isn't really backward Euler, because it doesn't backwards-evaluate the derivative. I've seen it called "semi-implicit Euler", which strikes me as inaccurate, since it isn't actually an implicit method. Again, there's no closed form analytic solution for backwards Euler.

jjd

2,140

March 01, 2006 05:43 PM

Also, Euler's method is not particular to displacement/velocity equations.

Typically implicit equations are solved with something like Newton's method or a "semi-implicit" Newton approach. Consider the equation y' = sin(y) for instance. Implicit Euler's method would give

y(n+1) = y(n) + h sin(y(n+1))

where you must solve for y(n+1).

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Difference Between Euler and Forward (Explicit) Euler

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Difference Between Euler and Forward (Explicit) Euler

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