Solving transcendental equations with discontinuities

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SUMMARY

The discussion centers on solving large transcendental equations of the form f(x) = 0, particularly when encountering discontinuities that hinder convergence using the Newton-Raphson method in Matlab. Participants highlight the challenge of finding all solutions to such equations, noting that no general numerical method exists for this purpose. The need for more specific details about the equation is emphasized to facilitate better suggestions for alternative methods.

PREREQUISITES
  • Understanding of transcendental equations and their properties
  • Familiarity with the Newton-Raphson method for root-finding
  • Basic knowledge of Matlab for numerical computations
  • Concept of discontinuities in mathematical functions
NEXT STEPS
  • Research alternative numerical methods for solving transcendental equations, such as the bisection method or fixed-point iteration
  • Explore Matlab's built-in functions for root-finding, such as fzero and fsolve
  • Study the implications of discontinuities on numerical methods and convergence
  • Investigate symbolic computation tools in Matlab for finding all roots of equations
USEFUL FOR

Mathematicians, engineers, and researchers dealing with complex transcendental equations, particularly those using Matlab for numerical analysis and seeking to understand the limitations of traditional root-finding methods.

wazzabi
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I have a fairly large transcendental equation which I write in the form f(x) = 0. I have attempted to use Newton Raphson to get some form of convergence but it often does not converge to the correct value. Plotting the function I found a discontinuity just after the solution. Is there a mathematical method which can deal with such transcendental equations, or is there even a method which can tell me all the solutions of an equation rather than just one of the roots?
I am using Matlab, if that helps.
Thanks in advance.
 
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wazzabi said:
Is there a mathematical method which can deal with such transcendental equations.

You haven't described your equation except to say that it was large, so you are essentially asking if there is a numerical method that can give all the solutions to any transcendental equation. I know of no numerical method that works with such generality. If you can give more specifics, perhaps someone can make a useful suggestion.
 

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