Runge鈥揔utta Methods for Monotone Differential and Delay Equations
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- 作者：P. E. Kloeden and J. Schropp
- 关键词：monotone dynamical systems ; delay equations ; Runge– ; Kutta methods
- 刊名：BIT Numerical Mathematics
- 出版时间：September 2003
- 出版年：2003
- 期刊代码：30_0006-3835
- 类别：mat
- 卷：43
- 期：3
- 页码：571-586
- 数据来源：sp
摘要
Classes of Runge–Kutta methods preserving the monotonicity of ordinary and delay differential equations are identified. Essentially, the vector b and the matrix A from the Butcher tableau should be such that all components of b are positive and all components of the matrix B(r)A, where B(r) is the inverse of the matrix I+rA, are nonnegative for sufficiently small positive r. The latter is satisfied by all explicit, diagonally-implicit and fully implicit Runge–Kutta methods for which all of the components of the matrix A, except those that are zero by definition, are positive.