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I was trying to solve a set of non linear equations using NSolve in mathematica. I got a result saying that no solution( {} ). My friend tried it in Matlab he was able to get a solution to the same set of equation for the same given parameters. Now my doubt is which one to trust?

I'm adding my functions bellow

    ClearAll[Evaluate[StringJoin[Context[], "*"]]]
    Needs["Utilities`CleanSlate`"]; 
    CleanSlate[]; 
    ClearInOut[];  

d[xt_, xv_, xo_, xb_] := (1189*(3*xv^2*(8/5 + xt/10) + (6*xv*xt*xo)/5 + 
      (6/5 - xt/10)*xo^2)*Cos[xb]^3)/3000000;  

ma1[xt_, xv_, xo_, xb_] := (1189*((48*xv^2)/5 + (3*xv^2*xt)/5 + 
      (16*xv*xt*xo)/5 + (18*xo^2)/5 - (3*xt*xo^2)/10)*Cos[xb]^2)/48000000;  

ma2[xt_, xv_, xo_, xb_] := (5/4)*xo^2*Cos[xb]*Sin[xb];  

q1[xt_, xv_, xo_, xb_] := (1189*(3*xt*((16*xv^2)/5 + (6*xo^2)/5) + 
      (1/10)*(-6*xv^2 - 16*xv*xt*xo + 3*xo^2))*Cos[xb]^3)/48000000;  

f11[xt_] := NSolve[{q1[xt, xv, xo, xb] == 0 && 
     d[xt, xv, xo, xb] - 133.05 == 0 && 
     ma1[xt, xv, xo, xb] - ma2[xt, xv, xo, xb] == 0}, {xv, xo, xb}, Reals, 
   WorkingPrecision -> 5]

f11[0.01] 

kindly any one help me

In Matlab he got these values xv=232.9328, xo =290.8831, xb=1.7934 10^(-4); And the solutions accuracy was up to 5 digits in matlab

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    $\begingroup$ You can quit the kernel instead of going through your four-step cleaning process. $\endgroup$
    – Roman
    Feb 17, 2020 at 20:12
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    $\begingroup$ Plugging in the Matlab values does not get one close to zero for d[xt, xv, xo, xb] - 133.05 or ma1[xt, xv, xo, xb] - ma2[xt, xv, xo, xb]. Assuming that Matlab correctly did what it was asked, maybe the code in Matlab wasn't quite the same as the formulas here. Showing the Matlab code could resolve that issue. $\endgroup$
    – JimB
    Feb 17, 2020 at 20:22

2 Answers 2

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Rationalized the numbers and use Solve

d[xt_,xv_,xo_,xb_]:=(1189*(3*xv^2*(8/5+xt/10)+(6*xv*xt*xo)/5+(6/5-xt/10)*xo^2)*Cos[xb]^3)/3000000;

ma1[xt_,xv_,xo_,xb_]:=(1189*((48*xv^2)/5+(3*xv^2*xt)/5+(16*xv*xt*xo)/5+(18*xo^2)/5-(3*xt*xo^2)/10)*Cos[xb]^2)/48000000;

ma2[xt_,xv_,xo_,xb_]:=(5/4)*xo^2*Cos[xb]*Sin[xb];

q1[xt_,xv_,xo_,xb_]:=(1189*(3*xt*((16*xv^2)/5+(6*xo^2)/5)+(1/10)*(-6*xv^2-16*xv*xt*xo+3*xo^2))*Cos[xb]^3)/48000000;

f11[xt_] := 
 Solve[{q1[xt, xv, xo, xb] == 0, d[xt, xv, xo, xb] - 13305/100 == 0, 
   ma1[xt, xv, xo, xb] - ma2[xt, xv, xo, xb] == 0}, {xv, xo, xb}]

f11[1/100] // N

gives

Mathematica graphics

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Use exact numbers and Solve: redefine

f11[xt_] := 
  Solve[{q1[xt, xv, xo, xb] == 0 && d[xt, xv, xo, xb] - 2661/20 == 0 &&
         ma1[xt, xv, xo, xb] - ma2[xt, xv, xo, xb] == 0}, {xv, xo, xb}]

and compute

f11[1/100]

gets you 8 solutions.

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