Suppression of numerically induced chaos with nonstandard finite difference schemes
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摘要
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.
论文关键词:65L06,34A50,Numerical instability,Nonstandard scheme
论文评审过程:Received 11 December 1998, Available online 20 September 2000.
论文官网地址:https://doi.org/10.1016/S0377-0427(99)00076-X