Solving Transcendental equation

Hi all,

I try to solve these system equations in matlab. I try to use fzero and fsolve but it did not work (R2010a). The system equation is

Re(λ)= μ=-αe^(-μ) cos(ω)
Im(λ)=ω=-αe^(-μ) sin(ω)

I appreciate for your help.

TN

[Grzegorz Knor]

Could you paste a piece of your code?

It would be easier to answer :)

[Walter Roberson]

You appear to have two equations in 3 unknowns ?

[tuan]

Yeah, that the hard problem in this two equation. If there is two unknown with equation so it is will be easy.

[tuan]

It just 2 variable mu and w, alpha is just a parameter, we can chose in any interval.

[Walter Roberson]

lambda and alpha are fixed values for any one problem? And you are looking for mu and w values that satisfy

lambda = alpha * exp(-mu + I*w)

Then

lambda/alpha = exp(-mu + I*w)

ln(lambda/alpha) = -mu + I*w

If mu and w are constrained to be real-valued then this would appear to have a single solution (unless alpha is 0).

Answer 1

[Walter Roberson]

You will need to indicate which variable(s) you are trying to solve for.

lambda = alpha * exp(-mu + I*w)

If you are trying to solve for alpha = 0, then that happens if either lambda = 0 or mu or w are infinite.

If you are trying to solve for lambda = 0, then that happens if either alpha = 0 or else mu and w are both zero.

You can also solve for mu or w being 0 without difficulty.

Answer 2

[tuan]

I don't think matlab can solve an equation with 2 variables like Walter said. I have the code that matlab can solve with 1 iteration but can not solve for 19 iteration. Any suggestion let me know thanks.

[a,u,v] = solve('-a*exp(-u)*cos(v)=u', 'v=a*exp(-u)*sin(v)', 'a=1')

it work well but with for loop

for a=0:0.1:1.8

        [a,u,v] = solve('-a*exp(-u)*cos(v)=u', 'v=a*exp(-u)*sin(v)','a')

    plot(a,u)

end

and it came out with this

Warning: 2 equations in 1 variables.

Warning: Explicit solution could not be found.

> In solve at 81

In Untitled2 at 3

a =

[ empty sym ]

u =

     []

v =

     []