An improvement on the positivity results for 2-stage explicit Runge–Kutta methods
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摘要
In this paper, we investigate the positivity property for a class of 2-stage explicit Runge–Kutta (RK2) methods of order two when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We also pay particular attention to monotonicity property. We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.
论文关键词：Ordinary differential equations,Initial value problems,Advection equation,Runge–Kutta methods,Positivity,Monotonicity
论文评审过程：Received 27 October 2009, Revised 9 May 2010, Available online 21 May 2010.
论文官网地址：https://doi.org/10.1016/j.cam.2010.05.020
