Article ID Journal Published Year Pages File Type
5776541 Applied Numerical Mathematics 2018 21 Pages PDF
Abstract

In [6] 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 two-stage second order modified Patankar-Runge-Kutta schemes.

Related Topics
Physical Sciences and Engineering Mathematics Computational Mathematics
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