How to solve implicit equations without the Symbolic Math Toolbox

Hi everyone,

I am trying to solve the following equation:

All the other variables are known except M. I am trying to solve for M. The MATLAB installation I am using is an academic version which doesn't have the Symbolic Math Toolbox. I would appreciate any help on this. Thanks.

Answer 1

[Matt J]

You can use fzero or fsolve, e.g.,

   a=2/(gamma+1);
   b=(gamma-1)/(gamma+1);
   c=gamma/2/(gamma-1);

   M=fzero(@(M) A/Astar - (a+b*M^2)^c/M, Mguess )

[Charles Kubeka]

I tried this:

A = 6 ;
gam  = 1.66 ;
a = (2/(gam+1));
b = (gam-1)/2 ;
c = gam /(2*(gam-1)) ;
fun = @(M)  A - (1/M)*(a*(1+(b*M^2)))^c ;
x0 = 2.5; 
z = fzero(fun,x0)

I get z = 10.1278 Which doesn't make sense if that is the value for M.

[Matt J]

It does make sense because if you evaluate fun at that point you will see that it satisfies your equation,

    K>> z = fzero(fun,2.5), val=fun(z)

    z =

       10.1278

    val =

         0

However, since the solution is non-unique, perhaps you were looking for the one closer to M=0,

    K>> z = fzero(fun,0.1), val=fun(z)

    z =

        0.1171

    val =

       1.7764e-15

[Charles Kubeka]

You're quite right Matt. Thanks a lot.

Answer 2

[Roger Stafford]

The matlab function 'fzero', which I am sure you do have, and which is explained at:

   http://www.mathworks.com/help/matlab/ref/fzero.html

will allow you to solve your problem. It does require an initial estimate of the approximate solution, and you can get that by first creating a plot of your expression as M varies to see roughly where it crosses the A/A* value, that is, where the difference between the two sides of your equation is zero.

Answer 3

[José Luis Vicens]

Creo que siempre debe construirse la gráfica con "ezplot". Y analizarla antes de comenzar a calcular. Evita muchas sorpresas y equivocaciones.