An improvement on the positivity results for 2-stage explicit Runge-Kutta methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Khalsaraei, M. Mehdizadeh^1,2 

[1] Ctr Wiskunde Informat Sci, NL-1098 XG Amsterdam, Netherlands

[2] Univ Tabriz, Fac Math Sci, Tabriz, Iran

关键词: Ordinary differential equations;    Initial value problems;    Advection equation;    Runge-Kutta methods;    Positivity;    Monotonicity;   

DOI  :  10.1016/j.cam.2010.05.020

来源: Elsevier

【 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. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free