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Alternative Equation Solving Packages


Alternative Equation Solving Packages

Anyone got any recommendations on equation solvers for engineering? Based on experience, if possible. I use Mathcad quite a lot, but its equation solving is not as flexible as say TK Solver or EES.


I used TK Solver 1.1 back in the day, but have hardly touched it in years. It was very good, especially back in the '80s. It was developed up to v5 by the late 90s or early 2000s, but then stuck there for nearly 20 years; I see UTS Systems brought out a new version, V6, late last year, but I didn't have time to get my head around it in the period of the free trial (work took me overseas for much of the last 6 months).


Some of my younger colleagues used Engineering Equation Solver (EES, from F-Chart Software) in college. I find the trial version (limitations: max 50 equation, OK; but also no save or edit) does not let me test it enough to decide on its capabilities.


Does anyone have experience of these and/or othe similar software; preferably in the same price bracket or cheaper.



23-Emerald III

"but its equation solving is not as flexible "


What type of flexibility do you need?

Mathcad can solve your (system of) equations numerically and (often) symbolically if there is a solution.

It will also work with units, which often helps to prevent errors. And Prime Express is free (but then allows only to solve linear systems of equations).



Indeed Mathcad can. But it needs the equations to be set up in a form it understands. TK Solver allowed me to set up equations in any order and as many as could be generated from the available data, over-specifying the system (more equations than unknown variables). I could then seek values for a specific variable and it would generate a (usually) minimal solution using only the necessary equations. If more than one set of equations could generate answers, it could offer all solutions.


I'm thinking of getting the current TK Solver as well as Mathcad. But since EES exists, I am seeking comments/advice as to which is the better, or indeed if there is another that is better.

Tool choice always boils down to what you're trying to do.  We have EES and for many things it is shockingly powerful.  It's iterative solver is fast and robust; far superior to Prime.  You can do a lot in EES, but it also has many limitations.  There are many rules about where you can put IFs, procedures, subroutines, etc.  So complicated programs can be tricky.  However, the parametric tables are brilliant (are you listening PTC???).  Plotting is competent but lackluster.  Built-in thermo properties.  It does units but does them rather clumsily; we usually don't take advantage of that.  Has a mode to view equations in symbolic form for checking, but the default/editor mode is just text.  Accepts equations in any order.  That's good and bad: makes life simple but encourages bad programming etiquette.  No symbolic capability.  For things like flow problems where you have to iteratively solve and then run 1000 cases of different parameters, it's hard to beat.   But it doesn't have the polish of mathcad.  


We gave up on TK solver a long time ago in favor EES.  It was clunky and solver wasn't as good.  But maybe it got better.


EES is written by a professor of University of Wisconsin.  He's very easy to contact and has made changes we've requested.  Can't do that with PTC.  Note, he's also retired and I've heard the plan is to sell f-chart at some point.  So changes may happen, good or bad who knows?  It's also a tool that evolved from a tool used to help students.  There's a new version almost weekly so I'm not sure of the quality checks that go into it; so that may be a negative for some industries. Not that I think it has more bugs than mathcad.


I think EES is worth having in the toolbox and not that expensive.  Mathcad, matlab, EES, and Excel (since we can't really fully avoid it) should be enough.  I'd add python as my next tool but haven't gotten there yet.  I use mathcad because I'm more after the documentation, appearance, units and ability to use the larger toolbox.  And I just like it's logic.  


Thanks. A very useful commentary. I'm afraid it has prompted a lot of specific questions.


You are quite critical of TK Solver. Do you recall which version you used, or when you bought it? As I commented, I last used TK Solver way back at version 1.1 (1980s?), but v6 was released last November. V6 looks quite different from v5, but I can't say if the changes address any of your criticisms.


With regard to EES, do you know what method is used for thermo properties? Is it based on Equations of State like CoolProp? or simpler interpolations? Does it just cover water, or also other fluids? Can EES link to external libraries like CoolProp or RefProps? Where units are used, are calculations done in a base system of units and converted for display (like Mathcad and SMath Studio do), or are calculations done in the units in which they are entered?


Interestingly, I see a version of EES is available for Android on Google Play Store. I must try it

I have very limited personal TK experience, but it was my company's default till about 15 years ago.  The stories I hear are that it was pretty terrible. The printouts I've seen were always confusing.

You can access EES's online help without having the software:



I think you'll find the answers to your questions there (and I don't know the answers directly). It has dozens of fluids. EES was developed for thermo students so they took some care in it, it appears.  Each fluid might be done differently, but here's one example:



 BENZENE provides high accuracy thermodynamic properties for benzene (Molar mass = 78.112 g/mole) using the Fundamental Equation of State presented in

 Thol, M., Lemmon, E.W., Span, R.

"Equation of state for benzene for temperatures from the melting line up to 750 K and pressures up to 500 MPa,"

provided as an extra edition for the 9th ATPC in Peking 2010, published by High Temperature - High Pressure

(draft paper provided by Dipl.-Ing. Monika Thol 


Reference State 

    h = 0 kJ/kg, s = 0 kJ/kg-K for ideal gas properties at the normal boiling point of 353.21635 K.  

    The reference state can be changed using the $Reference directive.


Range of applicability for equation of state:

  278.674 K < T < 750 K

0 < P < 500 MPa


Transport properties are provided using correlations given in:

Yaws, Carl L., ed. Chemical Properties Handbook. New York: McGraw-Hill, 1999. 


Surface tension data are provided using the information in:

Mulero, A., Cachadina, I, and Parra, M.

"Recommended Correlations for the Surface Tension of Common Fluids"

J.Phys. Chem Ref. Data, Vol. 41, No.4, 2012