Inhalt des Dokuments
Preprint 40-2007
Discrete Models for the Cube-Root Differential Equation
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")