Copyright © 2012 Xiong You. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In order to simulate gene regulatory oscillators more effectively, Runge-Kutta (RK) integrators are adapted to the limit-cycle structure of the system. Taking into account the oscillatory feature of the gene regulatory oscillators, phase-fitted and amplification-fitted Runge-Kutta (FRK) methods are designed. New FRK methods with phase-fitted and amplification-fitted updated are also considered. The error coefficients and the error constant for each of new FRK methods are obtained. In the numerical simulation of the two-gene regulatory system, the new methods are shown to be more accurate and more efficient than their prototype RK methods in the long-term integration. It is a new discovery that the best fitting frequency not only depends on the problem to be solved, but also depends on the method.