First off, thanks to the people who started this forum, and I apologize for this post being so long-winded.(adsbygoogle = window.adsbygoogle || []).push({});

I'm a retired engineer dabbling in engine simulation. The text I'm using as the foundation for the gas dynamics theory contains several nonlinear equation sets for each simulated scenario, followed by the answers for the unknown variables.

Using one particular set of 4 equations, I use the Newton-Raphson (N-R) method, as recommended by the author, and obtain the solution for the 4 unknowns. The problem is that my solution (the variable values) deviates substantially from the solution in the text even if I use the author's solved values--or something very near them in value--as my initial first guess. I also see this problem when using a commercial nonlinear solver. I thought a good test would be to plug the text solution values into each of the equations, expecting to see a "0" result for each, but instead, some results were far from zero. All of the coefficients match those in the text and I have verified that the equations are correct.

I trust the answers in the text; however, I suspect that something other than the plain vanilla N-R method is used, or that there is some "best fit" solution that doesn't require the equations to resolve to "0". I have sufficient intuitive knowledge of the system model that I could use some form of bracketing on the first guess for the unknowns, but I have no clue in this area.

Can anyone recommend a next step in trying to resolve this?

Frank

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# Nonlinear equation set

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