DISCRETE AND EXACT GENERAL SOLUTION FOR NONLINEAR AUTONOMOUS ORDINARY DIFFERENTIAL EQUATIONS

摘要

A discrete general solution and exact for nonlinear autonomous ordinary differential equations is proposed in this paper. Seemingly simple, the solution is based on Euler integrator. However, we used mean derivative functions instead of instantaneous derivative functions on this integrator. Empirically determining the mean derivative functions is not a trivial task. Therefore, it is necessary to solve a nonlinear parameter estimation problem by using some universal approximator of functions such as an artificial neural network or a fuzzy inference system. This article proposes to mathematically demonstrate these facts.