Piecewise Analytic Method (Solving Any Nonlinear Ordinary Differential Equation of 1st Order with Any Initial Condition)

The paper shows a new method which has the ability to solve any nonlinear 1^st order differential equation with any initial conditions. The method is called Piecewise Analytic Method (PAM). The accuracy of the method can be controlled according to our needs. A comparison between PAM and Runge-Kutta method is introduced which enhances the use of PAM. For non mathematician, they can now test their systems with any initial condition.