Approximate solution for kinetic differential equations

Mizukami, Akiyoshi; Isotani, Sadao; Rabbani, Said; Pontuschka, W. M.

doi:10.1007/bf02482398

Cited by 4 publications

(1 citation statement)

References 7 publications

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“…Previous research findings have shown that the solutions for the non-linear stability analysis of equations 1a and 1b are stable, following a hyperbolic path [18]. Mizukami et al [19] observed that these solutions can be represented by the sum of two terms. The first term leads to slow first order decay and the other to a fast decay.…”

Section: P P Pmentioning

confidence: 99%

An Algorithm to Optimize the Calculation of the Fourth Order Runge-Kutta Method Applied to the Numerical Integration of Kinetics Coupled Differential Equations

Isotani

Pontuschka²,

Isotani³

2012

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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 “large enough”. 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

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Section: P P Pmentioning

confidence: 99%