Suppression of numerically induced chaos with nonstandard finite difference schemes

✍ Scribed by Alicia Serfaty de Markus; Ronald E. Mickens

• Book ID: 104338943
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 481 KB
• Volume: 106
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00076-x

✦ Synopsis

It has been previously shown that despite its simplicity, appropriate nonstandard schemes greatly improve or eliminate numerical instabilities. In this work we construct several standard and nonstandard finite-difference schemes to solve a system of three ordinary nonlinear differential equations that models photoconductivity in semiconductors and for which it has been shown that integration with a conventional fourth-order Runge-Kutta algorithm produces numerical-induced chaos. It was found that a simple nonstandard forward Euler scheme successfully eliminates these numerical instabilities. In order to help determine the best finite-difference scheme, it was found useful to test the local stability of the scheme by direct inspection of the eigenvalues dependent on the step size.