MATLAB: Find positive roots of trigonometrical equation

roots

Hi everyone,

I am trying to find the positive roots of this kind of expression but using fzero I can only find one.

Is it possible to find 6 or more roots in matlab?

Best Answer

So lets see. You have a problem with infinitely many solutions, but no analytical solution. You want to find ALL of them. Infinity is a long way out. Do you have infinitely much memory to store them all? Infinitely much time to compute them all?

Use different starting values for fzero, computing one at a time, until you have found as many as you wish.

Related Solutions

MATLAB: Positive roots of trigonometric equation.

The function

     f(x) = x .* tan(x)

is continuous and strictly monotonically increasing in every interval [-pi/2,pi/2]+k*pi while the function

     g(x) = (a-x.^2) ./ (b + (a-x.^2)*c)

is continuous and strictly monotonically decreasing everywhere except at its unique pole xp.

Because f and g have opposite monotonicity in each interval [-pi/2,pi/2]+k*pi not containing xp, and because f(x) ranges from -inf to +inf there, the equation

                    f(x)=g(x)

will have exactly one solution in each of those intervals. These solutions are identically the roots of f(x)-g(x). The anomalous interval [-pi/2,pi/2]+k0*pi containing the pole xp can be handled by splitting it into 2 subintervals to the left and right of xp. Each of those subintervals must have exactly one root by the same monotonicity arguments.

Thus, you need simply loop over the first successive n of these intervals,subdividing the k0-th interval appropriately. In each interval, use fzero to find the unique root there.

MATLAB: Finding roots of trigonometric equation

Roots=solve(vr,theta,'maxDegree',4)

Best Answer

Related Solutions

MATLAB: Positive roots of trigonometric equation.

MATLAB: Finding roots of trigonometric equation

Related Question