Solving transcendental equations with discontinuities

  • Thread starter wazzabi
  • Start date
In summary, the individual is seeking help with a large transcendental equation which they have attempted to solve using Newton Raphson but have not been successful. They have also noticed a discontinuity in the function and are wondering if there is a mathematical method that can handle such equations and provide all solutions, rather than just one root. They are using Matlab and are looking for suggestions or solutions.
  • #1
wazzabi
1
0
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.
 
Mathematics news on Phys.org
  • #2
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.
 

FAQ: Solving transcendental equations with discontinuities

What is a transcendental equation?

A transcendental equation is an equation that involves mathematical functions that cannot be expressed in terms of a finite number of algebraic operations. Examples of transcendental functions include exponential, logarithmic, and trigonometric functions.

What are discontinuities in transcendental equations?

Discontinuities in transcendental equations occur when there is a sudden jump or break in the graph of the equation. This means that the function is not continuous at that point, and there may be different solutions on either side of the discontinuity.

How do you solve transcendental equations with discontinuities?

Solving transcendental equations with discontinuities can be a complex process and may require the use of numerical methods such as iteration or approximation. It is important to carefully analyze the function and its discontinuities to determine the most appropriate method for finding solutions.

What are some common techniques for solving transcendental equations with discontinuities?

Some common techniques for solving transcendental equations with discontinuities include the bisection method, the secant method, and Newton's method. These methods involve using a series of approximations to converge on a solution for the equation.

What are some real-world applications of solving transcendental equations with discontinuities?

Transcendental equations with discontinuities can arise in various fields of science and engineering, such as in modeling biological processes, analyzing financial data, and designing electronic circuits. Being able to solve these equations accurately is crucial for making informed decisions and predictions in these areas.

Similar threads

I Make Intelligent Initial Guesses for Newton-Raphson Programmatically
Replies
16
Views
2K
A How to use the Newton-Raphson method while keeping the sum constant?
Replies
2
Views
541
I Newton-Raphson Method With Complex Numbers
Replies
7
Views
2K
What is the Correct Approach to Solving the Deuteron Transcendental Equation?
Replies
14
Views
1K
I Convergence criterion for Newton-Raphson
Replies
9
Views
2K
I What is the difference between differential equations and functions?
Replies
8
Views
2K
Calculus Comparing "Calculus" and "Early Transcendentals" Textbooks for MST124
Replies
22
Views
6K
I Solving simultaneous vector equations
Replies
11
Views
2K
MHB Lachlan's question via email about the Bisection Method
Replies
1
Views
9K
MHB Solving Equations Using Bisection, Newton, and Secant Methods
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top