It is important to mention here that we have considered in our proof of the convergence of the new paradigm a discrete uniform probability distribution to prove all the results. Hence, we have assumed a uniform convergence of the numerical method where the probabilities and degrees of convergence or of chaos are equal to 0.5 when N = Nc | 2 =0.5Nc. This is certainly a simplified special case. Knowing that nonuniform probability distributions should be considered in other cases and in general where the numerical methods adopted do not converge uniformly like in the first case of the simulations where the probabilities and degrees of convergence or of chaos are equal to 0.5 when N = 0.08278Nc ≠ 0.5 Nc as it is shown in the simulations section. This will lead without any doubt to analogous conclusions and consequences similar to the simplified uniform convergence case as it is illustrated and shown in the simulations where other ODEs are considered.
Author(s) Details:
Abdo Abou Jaoudé,
Department of Mathematics and Statistics, Faculty of Natural and Applied Sciences, Notre Dame University-Louaize, Lebanon.