Newton Raphson Method for Finding Roots: Bessel's Function J0(x) near x=5

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In summary, the conversation discusses using the Newton-Raphson method to find the root of Bessel's function J0(x) near x=5, with the help of a PDF link. The homework equations involved in this method are the Newton-Raphson equation: x= a- f(a)/ f'(a). The first value to be substituted into this equation is 5, and the correct values can be found on page 16 of the attached link. The person asking for help has obtained an incorrect value of 3.895752124 for the first iteration and is seeking confirmation of the correct values. They have not provided details of their attempted solution.
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ruby_duby
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Homework Statement



Bessel's funtion J0(x) is assumed to have a root near x=5. Use the Newton raphson method to find this root to 3 decimal places by taking the first 4 terms of the series.

I have found this link which helps me solve the question:

http://www.vibrationdata.com/Newrap.pdf

PLEASE LOOK AT PAGES 15-16

Homework Equations



Newton raphson equation: x= a- f(a)[tex]/[/tex] f'(a)

The Attempt at a Solution



well I assume that as the root is near x=5, my first value that I substitute into the Newton raphson equation should be 5.

However, I get the value 3.895752124 which i do not think is right.

The table of values on page 16 of the link I have attached are the correct values I should have obtained, but I do not know where I am going wrong.

Can anyone confirm the values I should expect to obtain?
 
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  • #2
You are correct; 3.895752124 as the value for the first iteration is not correct; you should replicate the table in that attachment.

It's kinda hard to tell you where you went wrong because you didn't tell us what you did to get that erroneous value. What did you do, in detail?
 

Related to Newton Raphson Method for Finding Roots: Bessel's Function J0(x) near x=5

1. What is the Newton-Raphson method?

The Newton-Raphson method is a mathematical algorithm used to find the roots of a function. It is an iterative process that starts with an initial guess and then uses the derivative of the function to refine the guess until a root is found.

2. What is the main purpose of using the Newton-Raphson method?

The main purpose of using the Newton-Raphson method is to find the roots of a function, which can be used to solve equations or find critical values of a function.

3. What are the advantages of using the Newton-Raphson method?

The Newton-Raphson method has several advantages, including its quick convergence rate, its ability to find multiple roots of a function, and its versatility in solving a wide range of mathematical problems.

4. What are some potential issues or "troubles" with the Newton-Raphson method?

The Newton-Raphson method may encounter issues such as convergence failures, oscillating solutions, and sensitivity to initial guesses. It also requires knowledge of the function's derivative, which may not always be available.

5. How can the Newton-Raphson method be improved or modified to address these "troubles"?

Some modifications that can be made to the Newton-Raphson method include using a different initial guess, using a different iteration formula, or combining it with other methods for finding roots. Additionally, using a more accurate derivative approximation can also help improve the method's performance.

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