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Preprint 40-2007

Discrete Models for the Cube-Root Differential Equation

Source file is available as :   Portable Document Format (PDF)

Author(s) : Matthias Ehrhardt , Ronald E. Mickens

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 40-2007

MSC 2000

34C15 Nonlinear oscillations, coupled oscillators
34C25 Periodic solutions
65L07 Numerical investigation of stability of solutions
65L12 Finite difference methods

Abstract :
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.

Keywords : Nonlinear oscillations, periodic solutions, nonstandard finite differences, stability of numerical solutions

Notes :
submitted to: Neural, Parallel, and Scientific Computations (special issue on "Novel Difference and Hybrid Methods for Differential and Integro-Differential Equations")

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