Hi Sudipta,

Can you share your equations?

From my studies, I remember that the bisection method is mostly used for a function passing through zero. If you look for an extremum (minimum or maximum) of a function probably you will analyze the sign of the first derivative and also the sign of the second derivative to determinate if this is a maximum or a minimum.

Dear Halim, Thank you for your help. Actual equations are little bit complicated. Symbolically, I have:

f1(x,y,z) = 0, f2(x,y,z) = 0 and f3(x,y,z) = 0 typed THREE coupled transcendental equations. I want to use 'Bisection Method' to find different solutions.For example, m-th root of f1(x,y,z) = 0, n-th root of f2(x,y,z) = 0 and p-th root of f3(x,y,z) = 0 to find a solution (termed as 'mnp'). Can you help me to solve this coupled transcendental equations?

Can you write these equations in Matrix form? Then you will just need to resolve a Matrix inversion problem?

No, Sir. These are not linear equations, these are transcendental equation.

Can you use Taylor series to approximate some of the functions in the three equations?

If possible, you can also separate one equation into two functions and resolve graphically by finding the intersections of the two functions

Otherwise, I am not sure if you did your search in the internet but there is this document about multi-dimensional bisection method

http://www.mm.bme.hu/~bachrathy/MDBM_users_guide.pdf

Thank you, Respected Halim for this document. I will try to implement this in my problem.

Respected Halim, I read that PDF. It is found that if we want to solve system of transcendental equation, we have to use their code. But, I want to write the code myself.

If we want to use Taylor series approximation, we basically are doing newton's method (where initial guess is essential).

In my case, equations are coupled and I tried to separate three equations into two by eliminating one. But, it is not possible. Each equations has the basic form:

(S1*S2 - S5*S6)*(S3*S4 - S5*S6) = 0 where S1 to S6, all are transcendental equations. Sir, If I want to use bisection method, what will me my procedure. Can you please tell the steps. I'll try to implement that in MATLAB.

Dear Sudipta,

then I can suggest the Nelder-Mead method. The algorithm is described here:

https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method

if your equations use derivatives I can also suggest using Finite Difference method

Thank you Sir, I'll try to implement this method. Thank you once again.

Finally, I can solve system of transcendental equations using simple bisection method except HEM11 and HEM22 modes. Iterative process is used to obtain the convergence.  I can easily obtain the solution for HEM12 or HEM33 or HEM2,13 etc modes. In case of HEM11 and HEM22 modes, solutions regions are repeating but no solution is obtained. If one solution is satisfied, other one does not. But the same code is able to solve for other modes. I think, solutions for HEM11 and HEM22 modes got stuck in LOCAL minima. How can I overcome this problem in iteration procedure? Any suggestion(s)....