عنوان مجله
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International Journal of Nonlinear Analysis and Applications
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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. Based on general theory for
positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method)
positivity is not ensured when applied to the inhomogeneous linear systems and the same result is
regained on nonlinear positivity for this method. Here we mean by positivity that the nonnegativity
of the components of the initial vector is preserved. Nonstandard finite differences (NSFDs) schemes
can improve the accuracy and reduce computational costs of traditional finite difference schemes. In
addition to NSFDs produce numerical solutions which also exhibit essential properties of solution.
In this paper, we investigate the positivity property for nonstandard RK3 method when applied
to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential
equations (ODEs). We obtain new results for positivity which are important in practical applications.
We provide some numerical examples to illustrate our results
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