عنوان مجله
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Computational Mathematics and Mathematical Physics
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کلیدواژهها
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ordinary differential equations, initial value problems, nonstandard Runge–Kutta methods,
stability, elementary stable, positivity.
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چکیده
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When one solves differential equations, modeling physical phenomena, it is of great importance
to take physical constraints into account. More precisely, numerical schemes have to be designed
such that discrete solutions satisfy the same constraints as exact solutions. Nonstandard finite differences
(NSFDs) schemes can improve the accuracy and reduce computational costs of traditional
finite difference schemes. In addition NSFDs produce numerical solutions which also exhibit essential
properties of solution. In this paper, a class of nonstandard 2-stage Runge–Kutta methods of order
two (we call it nonstandard RK2) is considered. The preservation of some qualitative properties by this
class of methods are discussed. In order to illustrate our results, we provide some numerical examples
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