Step 23 - Theta method of time discretization when 2nd order time derivative

[Matthew Rich]

Hi 

My question is in relation to step 23. I am dipping my toes in the water with structural mechanics problems and I would like to avoid the quasistatic simplification. Now the example add velocity to reduce the order of the time derivative and proceeds  with the theta method. 

I wanted to know if that technique would be allowed if you replaced the 2nd order time derivative in the wave equation. The tutorial says it would be equivalent but I have not seen anything using the theta method that does not have just a 1st order time derivative. 

Is there a modification of the theta method that allows one to pretty much follow the steps of the tutorial but not reduce the order of the equation by variable substitution. 

Thanks in advance. 

Matt

[Wolfgang Bangerth]

Matthew -- I have to admit that I don't follow what specifically you are
asking. Are you asking whether the theta method can be used for second-order
problems without the reformulation to a first-order system? Or whether it can
be used for an altogether different equation?

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/