Piecewise analytic method (PAM)-(Published January 2012 by T. Abassy) is a new technique used for solving nonlinear differential equation. The advantages of PAM are( these points are proofed):
1. It gives a general analytic formula that can be used in differentiation and integration.
2. It can solve highly non-linear differential equation.
3. The accuracy and error can be controlled according to our needs very easily.
4. It can solve problems which other famous techniques can’t solve.
5. In some cases, it gives the exact solution.
6. ....
Please if you know information which is different let me know even if your answer is negative feedback.
Preprint Piecewise Analytic Method (PAM) is a New Step in the Evoluti...
Preprint Piecewise Analytic Method VS Runge-Kutta Method (Comparative Study)
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Dear Tamer Abassy,
Good article! I think that you need to add in the article a research (theorem) on the choice of the segment of convergence [t_m; t_{m+1}].
Best regards,
Prof. Pchelintsev.
Dear Prof. Alexander Pchelintsev PAM based on Taylor series. Taylor series is convergent as order -> infinity. In PAM, we control interval length and order according to our need of accuracy and time of calculation.
I'll put your comment in consideration.
Regards,
The radius of convergence of power series for nonlinear systems is bounded. It can be detected, for example, for the Lorenz and Chen systems. See my article https://www.researchgate.net/publication/289495998_A_New_Reliable_Numerical_Method_for_Computing_Chaotic_Solutions_of_Dynamical_Systems_The_Chen_Attractor_Case
You need to carefully explore of this question.
Dear Alexander Pchelintsev , I used PAM to obtain results for the system you solved. You can see a quick picture of my results in the attached Photo. If you wish, we can cooperate and compare my results and your results. I noticed that, you didn’t specify an upper pound limit of error. PAM will give you an analytic solution formula and upper pound error ….
I used Taylor Series which is proofed it is convergent.
One of the preprint papers which are mentioned above is published
Research Piecewise Analytic Method (PAM) is a New Step in the Evoluti...
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