I have developed new iterative method which converges ninth order. When apply this method in Matlab program it gives only second order. I did not understand why it is not in ninth order. My main questions: Theoretical convergence order and computational order convergence (COC) should equal always? If not equal what is the reason.
How do you know that your method is 9th order accurate? Mathematical proof?
If the assumptions you made during your proof hold for the problem you are trying to solve, then theoretical convergence order
I have verified theoretical order. By taylor series with help of mathematica software.
Can you share more about the iterative method?
If your test case has the same properties that were needed for the proof, then you should be seeing the correct convergence.
How are you doing the convergence calculation?
Numerical Analysis by Burden & Faires
Numerical Methods for Ordinary Differential Equaitons by Griffiths & Higham
How far away from 9 are you getting?
If you are confident about your theoretical side, perhaps you should investigate what is going on during the Matlab computations.
Could it be the newton iterative solver capping your convergence?
Newton's method is a order 2 method so that may be the problem.
You should be able to test this by using a linear problem and swap out the newton iterative solver with the true solution.
I suggested that you should check your MATLAB code, may be something might be missing.
check your Matlab program for the method. Mistake in your Matlab commands for iterative method.
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