%0 Journal Article
%T An Algorithm to Optimize the Calculation of the Fourth Order Runge-Kutta Method Applied to the Numerical Integration of Kinetics Coupled Differential Equations
%A Sadao Isotani
%A Walter Maigon Pontuschka
%A Seiji Isotani
%J Applied Mathematics
%P 1583-1592
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.311218
%X The kinetic electron trapping process in a shallow defect state and its subsequent thermal- or photo-stimulated promotion to a conduction band, followed by recombination in another defect, was described by Adirovitch using coupled rate differential equations. The solution for these equations has been frequently computed using the Runge-Kutta method. In this research, we empirically demonstrated that using the Runge-Kutta Fourth Order method may lead to incorrect and ramified results if the numbers of steps to achieve the solutions is not ˇ°large enoughˇ±. Taking into account these results, we conducted numerical analysis and experiments to develop an algorithm that determines the smallest non-critical number of steps in an automatic way to optimize the application of the Runge-Kutta Fourth Order method. This algorithm was implemented and tested in a variety of situations and the results have shown that our solution is robust in dealing with different equations and parameters.
%K Coupled Differential Equations
%K Runge-Kutta
%K Kinetics Equations
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=24328