Newton Raphson method for transcendental equations

This file computes roots of a given trancendental equation using the Newton-Raphson method.

Description

This m-file can be used to compute the root of any trascendental equation using the Newton-Raphson iterative method. The user defined parameters are the function itself, the initial point, the maximum number of permissible iterations and the error (tolerance).

• Required Products: Symbolic Math Toolbox
• MATLAB release: MATLAB 7.1.0 (R14SP3)
• Other Files: License.txt, ; license.txt, ; newton_raphson.m

[Abhishek Basu]

 

[Abhishek Basu]

I'd appreciate constructive suggestions about this code. I think the file could have been even more concise and resource efficient, so I'm looking forward to suggestions regarding what constructs might have made this submission even more useful. Feel free to drop in your ideas, and I'll try to incorporate them in my future works. Regards!

[Abhishek Basu]

I received a mail from Mohd. Shahrir Mohd. Sani today. He was seeking a solution to this problem: cosh(x)*cos(x) +1 = 0. It appears that the solution obtained from this program in this particular case isn't very accurate. The code seems to be working properly for most other functions.

[Matt Fig]

Three comments.

1. I do not see where you mention that this file needs the symbolic toolbox to run. It does. I wouldn't have downloaded it if I had known that because I don't have the symbolic toolbox. You should update the description to reflect this requirement.

2. Rating your own files is not good behavior. Everyone expects that an author likes his own files or he wouldn't have submitted them. Please don't try to trick people into thinking your file is esteemed by the community. Let others rate your files, then your skills and file quality can grow, and people looking for a quality file won't be misled by false ratings.

3. A numerical alternative that works for Shahrir's problem is:
f = @(x) cosh(x).*cos(x) + 1;
rt = newtzero(f); % Found on the File Exchange.
x = -8:.1:8;
plot(x,f(x),'b',rt,f(rt),'*r')

[Abhishek Basu]

Thanks for your feedback Matt. I hadn't noticed that the symbolic toolbox is necessary because my version of MatLab has most of the toolboxes installed. I'll update the description as you've pointed out. I'm a bit embarrassed by the self rating part, I was expecting a more active participation from the FEX community regarding comments and rating, which I didn't, so I made a rash move.

[Erdal Bizkevelci]

 

[Chandan]

Dear Mr. Basu

In the code you have directly computed the differential of a function with the help of MATLAB function,but how would you tackle cases when this differential becomes Zero. I hope that your code must incorporate ways to throw an exception error on your own or compute differential any other way. Infinite cycle is also a problem in certain cases. I suggest you incorporate some of the techniques to make this code more worthwhile.
Regards,