Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 235, Issue 1, Pages 137-143Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2010.05.020
Keywords
Ordinary differential equations; Initial value problems; Advection equation; Runge-Kutta methods; Positivity; Monotonicity
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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.
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