Talk:Newmark-beta method

Extended Mean Value Theorem
What is that supposed to be? Extended in which sense? Furthermore the sentence "[...] the extended mean value theorem must also be extended to the second time derivative." sounds rather unmathematical to me. What is meant is probably that the "extended mean value theorem" (whatever that is) has to be applied to the second time derivative, too.

134.169.77.186 13:57, 19 April 2007 (UTC) ezander


 * I found a reference to the Extended Mean Value Theorem here:
 * http://mathworld.wolfram.com/ExtendedMean-ValueTheorem.html
 * --Dario Mariani (talk) 03:06, 27 December 2007 (UTC)
 * --Dario Mariani (talk) 03:06, 27 December 2007 (UTC)


 * You're right. It's also under 'Mean value theorem/Cauchy's mean value theorem' here in wikipedia. I've changed the link to point to that subsection. 134.169.77.186 (talk) 07:20, 22 January 2009 (UTC) (ezander)

Notation
I honestly think the dots over u are incorrect if indeed the first line is an equation of motion the line should read, $$\dot{x}^{n+1}=\dot{x}^n+ \Delta t~\ddot{x}|_\gamma \,$$. Where a dot indicates a derivative w.r.t time. Comming from a CFD background we generally write discrete time points as superscripts, not subscripts, however, here I am not sure if this is standard for the solids community. Am I missing something? — Preceding unsigned comment added by Thunder852za (talk • contribs) 08:40, 8 June 2018 (UTC)


 * Ok so a colleague cleared this up $$ u= \Delta x \,$$. I think this should be stated up front.

Assessment comment
Substituted at 02:23, 5 May 2016 (UTC)

About the Dubious-Discuss tag
What kind of differential equations is the Newmark-Beta method intended for? Many methods are NOT SUITABLE for certain equations. How many times must the two equations be repeated in EACH step in order that they converge in that step? Is the method symplectic? ALWAYS? For example, $$\beta=0\,$$ reduces to the Velocity-Verlet method, which is symplectic (roughly conservative if acceleration=a(x)), but other values of $$\beta\,$$ doesn't seem to be symplectic if the two equations are computed once en each step.

Grausvictor (talk) 11:04, 9 January 2020 (UTC)

The constant average acceleration method is the Trapezoidal rule
This article refers to the constant average acceleration method, i.e., when $$\gamma = 0.5$$ and $$\beta = 0.25$$, as the Midpoint rule. This is untrue. It is actually the Trapezoidal rule. To be sure, one can substitute $$\gamma = 0.5$$ into the acceleration integral and obtain the familiar formula:


 * $$\dot{u}_{i} + (1 - \frac{1}{2})(\Delta t) \ddot{u}_{i} + \frac{1}{2} (\Delta t) \ddot{u}_{i + 1} = \underbrace{\dot{u}_{i} + \frac{1}{2} (\Delta t) (\ddot{u}_{i} + \ddot{u}_{i + 1})}_{\text{Trapezoidal rule}}$$.

I would make the correction, but I am not sure what point the original author was trying to make when referencing the "middle point rule." My understanding is that it is a fundamentally different, explicit integration rule. — Preceding unsigned comment added by Crswong888 (talk • contribs) 06:09, 22 February 2021 (UTC)