Solving 5 nonlinear equations with fsolve

Question

Joaquim Monteiro 2015-12-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/261787-solving-5-nonlinear-equations-with-fsolve

评论： Joaquim Monteiro 2015-12-28

I'm a newbie in matlab. I'm trying to solve the following nonlinear equation system but I don't know how:

Qevap-((500+0.85*(((0.711+0.56*15/100+0.73*(15/100)^2)*5.67*10^(-8)*(25+273.15)^4*(1-cos(30*pi/180))/2)-5.67*10^(-8)*(25+273.15)^4))*1.6*0.8*(1-0*2)*1-1.6*((32+6.4*2)*(Te-25)))=0;

Qcond-(2068.5072425+(-20.1259571429)*Tc+0.0701428571*Tc^2+(56.5615102375+(-0.0892494524)*Tc+(-0.0013878571)*Tc^2)*Te+(0.669960831250007+(-0.001477845238096)*Tc+0.000000357142857*Tc^2)*Te^2)=0;

Wcomp-(373.160515+(-0.7728)*Tc+0.0378095238*Tc^2+((-4.03604873)+0.2014116*Tc+0.0005034286*Tc^2)*Te+((-0.22703617375)+0.003774373809524*Tc+(-0.000001214285714)*Tc^2)*Te^2)=0;

Qcond-(70*(Tc-40))=0;

Qcond-(Wcomp+Qevap-12*(Tc-20))=0;

I already saw the help documentation but I don't understando how to solve for 5 equations.

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Answer 1

John D'Errico 2015-12-28

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https://ww2.mathworks.cn/matlabcentral/answers/261787-solving-5-nonlinear-equations-with-fsolve#answer_204424

编辑：John D'Errico 2015-12-28

在 MATLAB Online 中打开

I would just use the symbolic toolbox, finding 8 solutions.

syms Qevap Te Wcomp Qcond Tc
E1 = Qevap-((500+0.85*(((0.711+0.56*15/100+0.73*(15/100)^2)*5.67*10^(-8)*(25+273.15)^4*(1-cos(30*pi/180))/2)-5.67*10^(-8)*(25+273.15)^4))*1.6*0.8*(1-0*2)*1-1.6*((32+6.4*2)*(Te-25)))==0;
E2 = Qcond-(2068.5072425+(-20.1259571429)*Tc+0.0701428571*Tc^2+(56.5615102375+(-0.0892494524)*Tc+(-0.0013878571)*Tc^2)*Te+(0.669960831250007+(-0.001477845238096)*Tc+0.000000357142857*Tc^2)*Te^2)==0;
E3 = Wcomp-(373.160515+(-0.7728)*Tc+0.0378095238*Tc^2+((-4.03604873)+0.2014116*Tc+0.0005034286*Tc^2)*Te+((-0.22703617375)+0.003774373809524*Tc+(-0.000001214285714)*Tc^2)*Te^2)==0;
E4 = Qcond-(70*(Tc-40))==0;
E5 = Qcond-(Wcomp+Qevap-12*(Tc-20))==0;
result = solve(E1,E2,E3,E4,E5)
result = 
  Qcond: [8x1 sym]
  Qevap: [8x1 sym]
     Tc: [8x1 sym]
     Te: [8x1 sym]
  Wcomp: [8x1 sym]
vpa(result.Qcond)
ans =
                                     206096.8437659089227610369512416
                                   -79872.272069545160204450007603734
                                    1480.0008801680255734628586801899
                                    13408.004024141292656129583676207
                                    10377.849121673682022577971691659
                                     118026.5590524018573505429634831
1430.3277485980905870082908902277 - 10413.553488331644261070420163996i
1430.3277485980905870082908902277 + 10413.553488331644261070420163996i