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Discrete Models for the Cube-Root Differential Equation

Ehrhardt, Matthias; Mickens, Ronald E.

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

Our main purpose is to construct one standard and three nonstandard finite difference schemes for the cube-root differential equation. After an analysis of the general qualitative features of the solutions to this equation and a calculation of the exact period, we study the stability of the numerical solutions for the four discretization schemes. Our general conclusion is that the standard forward-Euler method gives unstable numerical solutions, while the three nonstandard schemes provide suitable integration procedures.