An attractive idea is to combine the reliability of the bisection method with the speed of Newton's method. Such a combination is implemented by running the bisection method until we have a narrow interval, and then switch to Newton's method for speed.
Write a script that implements this idea. Start with the bisection method with an interval [a,b] and switch to Newton's method when the current interval in the bisection method is a fraction ‘s’ of the initial interval (when the interval has length s(b−a)). Potential divergence of Newton's method is still an issue, so if the approximate root jumps out of the narrowed interval (where the solution is known to lie), one can switch back to the bisection method. The value of ‘s’ can be set by the user.
Refer to the assignments for the Bisection and Newton’s method for details on those methods. You may utilize any work done on those assignments.
Find the solution of f(x)=cos(2x)+sin(√x)=0 over 2<x<5 using the combined method as follows:
Define a maximum number of iterations (103) allowed and an error tolerance ϵ (10-6) and fraction of the original rang s=0.1.
Pseudo code
Define an initial range of ‘a’ and ‘b’, and convergence ϵ. Define the fraction ‘s’.
If the current range (b-a) is greater than s(b-a) (the original ‘b’ and ‘a’, then use the bisection method to determine new range (new ‘a’ and ‘b’)
If the current range is less than or equal to s(b-a), then use Newton’s method to solve for the root. (a good initial guess is the average of the current range)
If the current guess for Newton’s method goes outside the current range, then use bisection to get a new range.
Once the root has been found (refer to the Newton’s method), output messages as per the Newton’s method.
Hi my friend, I can help you to develope the algorithm that use bisection and Newton Method to improve the algorithm with Matlab. If it's in my hands I can do it as fast as possible. If you have previous algorithms developed I can use them or I can also develope. Tell me more about it
Hi
"Don't think I cannot work"
Zubair Ghafoor is here. I am an Electrical Engineer having four years of experience in the Matlab. I will provide you with the best service of the work.
I have already done so many projects related to Matlab.
I have seen the whole script requirements, as per you want, can you give me a reference to the complete question, I will write this code for you. but need more information.
If you didn’t like the work or you have some argument with the work then the money payback is granted.
Must contact for more details.
Thanks.
PhD in electrical engineering (signal processing) from Canada.
MSc mathematics (numerical methods).
4 years assistant professor in the mathematics and engineering physics department.
10 years R&D engineer in Toronto, Canada.
I was teaching numerical methods for 4 years in the faculty of Engineering.
Dear project manager,
I am Navid graduated from the industrial information engineering school, the department of Politecnico di Milano, in Italy. I have read your project description and I found out that I can effectively help you to carry out this project. I have massively experience in MATLAB and Python programming and I can hugely help you with this project. It is a great pleasure to keep in touch with you for further information about your project.
Best regards
Navid
I have done a very similar project to this on Matlab and will be able to finish this within 2 days. I will also be able to provide comments and any other required technical help.
Hello
I am a professional mathematician having 9 years of teaching and project work experience in MATLAB.
You have come up with a nice idea which I can surely automate using MATLAB.
Hi,
Yor Project reminds me of Numerical Method subject during my Master's in Mechanical Engineering at IIT Ropar.
I had worked on programming various Numerical methods (including Bisection & Newton Raphson) on MATLAB. The simplicity of these methods accompanied by the programming (for large iterations) always fascinates me.
I would really like to work on your project.
Thanks