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I am using Modelica for solving a system of equations for heat transfer problems, and one of them is radiation which is written as
Ta^4-Tb^4
Can someone say if it is computationally faster solving a system with the equation written as:
(Ta-Tb)(Ta+Tb)(Ta^2+Tb^2)
?
There cannot be a definitive answer to this question. This is because the Modelica specification is used to formally define the problem statement but it says nothing about how tools solve such equations. Furthermore, since most Modelica tools do symbolic manipulation anyway, it is hard to predict what steps they might take with such an equation. For example, a tool may very well transform this into a Horner polynomial on its own (without your manual intervention).
If you are going to solve for the temperatures in such an equation as a non-linear system, be careful about negative temperature solutions. You should investigate the “start” attribute to specify initial (positive) guesses when these temperatures are iteration variables in non-linear problems.