2012
DOI: 10.4236/am.2012.311218
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An Algorithm to Optimize the Calculation of the Fourth Order Runge-Kutta Method Applied to the Numerical Integration of Kinetics Coupled Differential Equations

Abstract: 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 … Show more

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Cited by 5 publications
(3 citation statements)
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“…It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge-Kutta method while Runge-Kutta 4 th order meaning that the local truncation error is on the order of O(h 5 ), while the total accumulated error is order O(h 4 ). The values of KM and Vmax were estimated by solving Equations 2 and 3 concerning the substrate concentration and product formation based on Euler's and Runge-Kutta 4 th order methods by using Microsoft Office Excel [23]. In this study, pectin was used as the substrate while the product that produced was methanol.…”
Section: Euler's and Runge-kutta 4 Th Ordermentioning
confidence: 99%
“…It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge-Kutta method while Runge-Kutta 4 th order meaning that the local truncation error is on the order of O(h 5 ), while the total accumulated error is order O(h 4 ). The values of KM and Vmax were estimated by solving Equations 2 and 3 concerning the substrate concentration and product formation based on Euler's and Runge-Kutta 4 th order methods by using Microsoft Office Excel [23]. In this study, pectin was used as the substrate while the product that produced was methanol.…”
Section: Euler's and Runge-kutta 4 Th Ordermentioning
confidence: 99%
“…Equation (15) was solved numerically using ode 45 solver in MatLab and obtained the three time series S(t), I(t) and I v (t) in Figure 2. This solver function implements a fourth order Runge-Kutta method with a variable time step for efficient computation (Isotani et al, 2012).…”
Section: Wavelet Power Spectrummentioning
confidence: 99%
“…Vários estudos mostram a eficiência de métodos de passo único para resolução de problemas rígidos (Kaps e Rentrop, 1979), (Sandu et al, 1997), (Hairer e Wanner, 1999), (Loch et al, 2013c), (Brugnano et al, 2015), (Liao, 2015). Na Física Nuclear, os métodos de Runge-Kutta explícitos, tais como RK 4-4 e RK 4-5, são bastante utilizados para resolução de EDOs (de Carvalho, 2006), (Claro, 2011), (Isotani et al, 2012), (Takai e Hagino, 2015). Porém, vimos no capítulo 2 que problemas rígidos sugerem o uso de métodos implícitos para sua resolução.…”
Section: 2unclassified