Solving Non-Linear Equations in Matlab by Iteration

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Veronica Gabriel
Veronica Gabriel 2023-5-2
编辑： Torsten 2023-5-4
I am doing my matlab project and I am stuck in this part. This is a part of my code:
dhO2out= r*(O2a*(taf-tref)+(O2b/2)*(taf^2 - tref)+O2c*log(taf-tref)+O2d*(taf-tref)*log(taf-tref)-(taf-tref)+(O2e/3)*(taf^3 - tref));
dhN2out= r*(N2a*(taf-tref)+(N2b/2)*(taf^2 - tref)+N2c*log(taf-tref)+N2d*(taf-tref)*log(taf-tref)-(taf-tref)+(N2e/3)*(taf^3 - tref));
dhCO2 = r*(CO2a*(taf-tref)+(CO2b/2)*(taf^2 - tref)+CO2c*log(taf-tref)+CO2d*(taf-tref)*log(taf-tref)-(taf-tref)+(CO2e/3)*(taf^3 - tref));
dhH2O = r*(H2Oa*(taf-tref)+(H2Ob/2)*(taf^2 - tref)+H2Oc*log(taf-tref)+H2Od*(taf-tref)*log(taf-tref)-(taf-tref)+(H2Oe/3)*(taf^3 - tref));
syms taf
hp = dhO2out+dhN2out+dhCO2+dhH2O == sum (v10);
s = vpasolve (hp,taf,'Random',true);
disp ('The adiabatic flame temperature is (K): ')
disp (s)
I am using the function vpasolve, but it's giving me unspecified answer. I asked my professor and he told me that I can use iteration (like Newton raphson method) to find taf. But how do I do this in matlab? - Pls help, THANK YOU.

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采纳的回答

Torsten
Torsten 2023-5-2
编辑：Torsten 2023-5-2
First step:
Give numerical values to all variables except "taf"
Second step:
Plot dhO2out+dhN2out+dhCO2+dhH2O - sum (v10) as a function of taf to approximately locate the zero:
dhO2out= @(taf) r*(O2a*(taf-tref)+(O2b/2)*(taf.^2 - tref)+O2c*log(taf-tref)+O2d*(taf-tref).*log(taf-tref)-(taf-tref)+(O2e/3)*(taf.^3 - tref))
dhN2out= @(taf) r*(N2a*(taf-tref)+(N2b/2)*(taf.^2 - tref)+N2c*log(taf-tref)+N2d*(taf-tref).*log(taf-tref)-(taf-tref)+(N2e/3)*(taf.^3 - tref));
dhCO2 = @(taf) r*(CO2a*(taf-tref)+(CO2b/2)*(taf.^2 - tref)+CO2c*log(taf-tref)+CO2d*(taf-tref).*log(taf-tref)-(taf-tref)+(CO2e/3)*(taf.^3 - tref));
dhH2O = @(taf) r*(H2Oa*(taf-tref)+(H2Ob/2)*(taf.^2 - tref)+H2Oc*log(taf-tref)+H2Od*(taf-tref).*log(taf-tref)-(taf-tref)+(H2Oe/3)*(taf.^3 - tref));
hp = @(taf) dhO2out(taf)+dhN2out(taf)+dhCO2(taf)+dhH2O(taf) - sum (v10);
taf = tref+1:tref+500;
plot(taf,hp(taf))
Third step:
Locate taf from the graph, set it as taf0 and use fzero to solve:
taf0 = ...;
taf = fzero(hp,taf0)
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Veronica Gabriel
Veronica Gabriel 2023-5-4
Hi, thank you! I already found it - but it is now giving me an error when I run it.
Exiting fzero: aborting search for an interval containing a sign change
because complex function value encountered during search.
(Function value at -84 is -3111.2844+26.17844i.)
Check function or try again with a different starting value.
taf =
NaN
Torsten
Torsten 2023-5-4
编辑：Torsten 2023-5-4
Where does the plot of
dhO2out(taf)+dhN2out(taf)+dhCO2(taf)+dhH2O(taf) - sum (v10)
cross the x-axis when you do the plot as I wrote you should ?

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