CANNOT FIND EXPLICIT SOLUTION

A=6.30; B=9.40;delta=0.34;
EG0=1.519;a=0.472*10^(-3);seta=230;p=2.44;
T1=293.15;T2=373.15;
y=900*10^(-9):10^(-9):1700*10^(-9);
h=4.13566*10^(-15);
EG1=EG0-a*seta*0.5*(power(1+((2*T1)/seta)^p,1/p)-1);
EG2=EG0-a*seta*0.5*(power(1+((2*T2)/seta)^p,1/p)-1);
EG3=EG0-a*seta*0.5*(power(1+((2*300)/seta)^p,1/p)-1);
syms nr
c=299792452;
hw=(h*c)./(nr*y);
x1=hw/EG1; x2=hw/(EG1+delta);
fx1=power(x1,-2).*(2-sqrt(1+x1)-sqrt(1-x1));
fx2=power(x2,-2).*(2-sqrt(1+x2)-sqrt(1-x2));
eq=nr^2-A*(fx1+0.5*fx2*(EG1/(EG1+delta))^1.5)-B
solve(eq,nr);

I don't know how to solve the 'nr'. The only unknown number is nr, But MATLAB says 'Cannot find explicit solution.' In solve(line 316). how can I solve it?

Answer 1

[Jesús Zambrano]

Hi Jiyoung,

What I see from your code is that there is a variable 'y' which is a vector of 801 elements. Thas makes you to have, after following the rest of lines in the code, 801 elements in your 'eq'. I guess you want to solve each element of 'eq' for 'nr', right?

If so, then put the solve in a for-loop that executes it for each elements of the vector 'eq'. Note that when you solve it for the first element, i.e. eq(1), you will get:

solve(eq(1),nr)
 
ans =
 
                                                                      -3.4055195247431015387149927562818
                                                                       3.4055195247431015387149927562818
                              - 0.23371803267167591292641549805172 - 0.84472889222660849307066527049399i
                              - 0.23371803267167591292641549805172 + 0.84472889222660849307066527049399i
                                - 0.2188548808156796407592891677842 - 1.2614207237196718736658771540873i
                                - 0.2188548808156796407592891677842 + 1.2614207237196718736658771540873i
                               - 0.2009831298087114922620258832011 - 0.63984098829267138761023290039748i
                               - 0.2009831298087114922620258832011 + 0.63984098829267138761023290039748i
                             - 0.095279410850735997800776403284443 - 0.55834240108227279261730458860913i
                             - 0.095279410850735997800776403284443 + 0.55834240108227279261730458860913i
                             - 0.073816698835835126920532553463148 - 0.67770646926384383539367083081255i
                             - 0.073816698835835126920532553463148 + 0.67770646926384383539367083081255i
                             - 0.035279698323879157508614161138525 - 0.50104079719727104870701077365044i
                             - 0.035279698323879157508614161138525 + 0.50104079719727104870701077365044i
                           - 5.3926038442842603885567382392378e-33 - 0.58125154905583862889817538507886i
                           - 5.3926038442842603885567382392378e-33 + 0.58125154905583862889817538507886i
                           - 7.7037197775489434122239117703397e-34 - 0.84730569050904191778663882760979i
                           - 7.7037197775489434122239117703397e-34 + 0.84730569050904191778663882760979i
 0.000000000000000000000000000000014637067577342992483225432363645 - 0.44729847829331506330489730016435i
 0.000000000000000000000000000000014637067577342992483225432363645 + 0.44729847829331506330489730016435i
                               0.035279698323879157508614161138514 - 0.50104079719727104870701077365046i
                               0.035279698323879157508614161138514 + 0.50104079719727104870701077365046i
                               0.073816698835835126920532553463143 - 0.67770646926384383539367083081256i
                               0.073816698835835126920532553463143 + 0.67770646926384383539367083081256i
                               0.095279410850735997800776403284446 - 0.55834240108227279261730458860914i
                               0.095279410850735997800776403284446 + 0.55834240108227279261730458860914i
                                 0.2009831298087114922620258832011 - 0.63984098829267138761023290039749i
                                 0.2009831298087114922620258832011 + 0.63984098829267138761023290039749i
                                  0.2188548808156796407592891677842 - 1.2614207237196718736658771540873i
                                  0.2188548808156796407592891677842 + 1.2614207237196718736658771540873i
                                0.23371803267167591292641549805172 - 0.84472889222660849307066527049399i
                                0.23371803267167591292641549805172 + 0.84472889222660849307066527049399i
                                

Also, try to use the command 'vpa' so to simplify coefficient on symbolic fractions before use 'solve'. This might reduce a lot the time it takes for 'solve' to give the numerical results.

Hope this can help to solve the problem.

[Walter Roberson]

However if you are going to use vpa to simplify the coefficients then you should probably be using vpasolve. solve() is for exact solutions as much as possible.

[Jesús Zambrano]

Good suggestions, thanks!

[Jiyoung Lee]

I understood. Thank you so much! However, Can I ask just one more question? Actually, my final destination is plot (y,nr1). would you advise about my code?

my modified code is following:

nr1=zeros(1:801);
for i = 1:801
     nr1(1,i)=vpasolve(eq(i),nr);
end

[Jesús Zambrano]

Sure, then plot 'nr1' agains 'nr'.