Part of the answer in red [attached]
Will be back later on. Inversing a function
is sometimes difficult, but always possible.

Cheers, Jean 4.2.5 Steel temperature development.sm (26kb) downloaded 41 time(s).

Thank you for helping me.

I just added the Maple plugin. It now tells me the input format is not valid...

This is the result I get.. I don't understand..

Problem 1: How can I solve the differential equation 4.25 with respect to
θa(t)? I want to be able to calculate the development of temperature
in a steel member as a function of time.

Not sure I understand, θa(t) does not appear in 4.25 ?

You are correct. θa is not included in 4.25.

Please have a look at the latest workbook from post #22. Radovan has helped me arrange all the expressions into a ODE solver, however, there is still one problem.

I appreciate all your help!

You are solving for θ.a wrt c.a which in turn depends upon θ.a itself
That's too "circular". You can solve iteratively within a loop for
some predefined "c.a" around the peak 735

425specificheat.sm (773kb) downloaded 29 time(s).

Try this one with another solver - dn_GearsBDF (it will escape from the critical regions - possible division by zero). Actually, it will work for all the four c.a() but not if you put them in the condition statement.

425specificheat-2-corr.sm (739kb) downloaded 24 time(s).

Regards,
Radovan

Your differential equation is dθ.a/dt = D(t,θ.a) = f(t,θ.a,c(θ.a)). Your goal is to find θ.a(t) by solving this initial problem in the range t[0,150] provided the initial condition θ.a(0)=20 finding θ.a(0+..150). I do not know how else to explain this to you, sorry.

Regards,
Radovan

P.S. The main problem here IMHO is why the solvers can not accept conditional statements for c(θ.a) taking into account the numerical nature of the solving this problem but, on the other hand, the individual c(θ.a) causes no problem.

Yes, Smath solves but there are few points to understand.
The conditional 'ca' shows simply the system has 4 different DE solutions that depend
upon θ ... in other words the DE is not consistent. In Mathcad 11 Tom G. did a setup
for ordinary RK to take conditional. Not sure if I can retrieve, not sure either if
possible to code Smath ... from recollection, the system was consistent, i.e: a single
solution. Say otherwise, in there is like solving for different "phase phenomenon'

Excel is just given the data table to get a plot. Ordinary people understand Excel
because it's not a math tool, they understand like a grocery list. Any and all standards
are tabulated, thus instead of using tabulation from Peter, Bill, Arthur ,,, Excel
is convenient to get the hard copy.

The sol900 does not survive very far !

Cheers, Jean

425specificheat-2-corr [Piecewise].sm (773kb) downloaded 26 time(s).

Well done ! just add some of the EuroCode equations number ...

Cheers, Jean

testing 4 ode [Gorgeous].sm (25kb) downloaded 33 time(s).