Solving transcedental equation

[russel.arnold]

i want to solve tan (f(x)) = g(x) ..also i want to determine all the possible solutions!
which numerical method i should use?

 

[DuncanM]

There is no one answer.

Since tan has an infinite number of asymptotes, the first questions I'd have to ask is, will you be considering a particular range? Once you have a range, any numerical method could do the job.

I'd also wonder how accurate do you need solutions? To two decimal places? Three? Four? . . . If you didn't need a high degree of accuracy, perhaps even a graphical approach would work for you.

 

[russel.arnold]

yes, i will be considering tan from 0 to infinity, i.e all possible branches

and i need my solutions to be accurate. hence graphical approach won't work :(

 

[Floid]

I would first evaluate f(x) and then use that result in the series expansion of tangent taken however far you want to get the accuracy you desire to solve.

That will work for all possible solutions.

 

[CellCoree]

There are several numerical methods that can be used to solve transcendental equations, such as the bisection method, the Newton-Raphson method, and the secant method. The best method to use will depend on the specific equation and the initial values given. It is recommended to try different methods and compare the results to determine the most accurate and efficient approach for your specific equation. Additionally, it is important to keep in mind that transcendental equations can have multiple solutions, so it is important to check for all possible solutions when using numerical methods.