Newmark-Beta vs Predictor Corrector

In summary, the conversation discusses the Newmark-Beta method, which is used for integrating coupled, second order differential equations. The method can be implemented as a predictor/corrector or as just Newmark alone, causing confusion. The Newmark method is not the same as a Predictor Corrector method, although some sources may use both together. The conversation also includes links to statements of Newmark, one that mentions predictor/corrector and one that does not. Ultimately, it is clarified that the two methods are not the same.
  • #1
JTC
100
6
Hello,

I am teaching myself various numerical methods for integrating coupled, second order differential equations.
I am looking at Newmark-Beta methods

Sometimes I see Newmark Beta implemented as a predictor/corrector method.
Sometimes I see just Newmark methods alone.

And I get confused.

What IS the Newmark Beta method?
Is it so inextricably tied to the notion of predictor corrector that it is one and the same?

Or, are some of the sources just applying a "predictor/corrector" improvement on TOP of the Newmark scheme.

Here is a statement of Newmark (and I see no reference to predictor corrector)
https://en.wikipedia.org/wiki/Newmark-beta_method

Here is a statement of Newmark that launches right into prediction and correction
http://opensees.berkeley.edu/wiki/index.php/Newmark_Method

What is the Newmark method?
 
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  • #2
Sorry...

Thanks for the bump, but I figured it out a few days later, and forgot about this post

My assumption was correct...

The Newmark Method (NM) is NOT the same a a Predictor Corrector (PC). I just happened to have LEARNED about both at the same time where NM was implemented in a PC style.
 

Related to Newmark-Beta vs Predictor Corrector

What is the difference between Newmark-Beta and Predictor Corrector methods?

The Newmark-Beta method and Predictor Corrector method are both numerical integration techniques used to solve differential equations. However, the main difference between the two is that Newmark-Beta is an implicit method while Predictor Corrector is an explicit method.

Which method is more accurate?

Both methods have their own advantages and disadvantages in terms of accuracy. Newmark-Beta tends to be more accurate for stiff systems, while Predictor Corrector may be more accurate for non-stiff systems. Ultimately, the accuracy of either method depends on the specific problem being solved and the parameters chosen.

Which method is faster?

Predictor Corrector tends to be faster than Newmark-Beta, as it requires fewer calculations per time step. However, the speed also depends on the complexity of the problem being solved and the parameters chosen.

When should I use Newmark-Beta over Predictor Corrector?

Newmark-Beta is a good choice for solving stiff systems or problems with strong damping. It also tends to be more stable than Predictor Corrector for larger time steps. However, it may be more computationally expensive and slower than Predictor Corrector for some problems.

What are the limitations of these methods?

Both Newmark-Beta and Predictor Corrector have limitations, such as being sensitive to the choice of time step and initial conditions. They may also struggle with problems that have rapidly changing forces or discontinuities. It is important to carefully consider the specific problem and choose the appropriate method based on its strengths and limitations.

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