Positivity-preserving adaptive Runge–Kutta methods

Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the is solved numerically. We propose to ensure positivity other by applying Runge-Kutta integration which method weights are adapted order enforce bounds. The chosen at each step after calculating stage derivatives, a way that also preserves (when possible) of accuracy method. choice given solution linear program. investigate different approaches choosing considering adding further constraints. provide analysis properties methods with perturbed weights. Numerical examples demonstrate effectiveness approach, including application both stiff and non-stiff problems.