Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Order Conditions for modified Patankar-Runge-Kutta schemes   In \cite{BDM2003} the modified Patankar-Euler and modified
Patankar-Runge-Kutta schemes were introduced to solve positive and conservative
systems of ordinary differential equations. These modifications of the forward
Euler scheme and Heun's method guarantee positivity and conservation
irrespective of the chosen time step size. In this paper we introduce a general
definition of modified Patankar-Runge-Kutta schemes and derive necessary and
sufficient conditions to obtain first and second order methods. We also
introduce two novel families of second order modified Patankar-Runge-Kutta
schemes.

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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin