Analytical exponential model for stochastic point kinetics equations via eigenvalues and eigenvectors

A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems

“…A ramp reactivity input, ( ) = 0.1 , is considered with kinetic parameters listed in Table 1. Table 3 shows a comparison between our tenthorder SCS method, stiffness confinement method SCM, −weighting method [21], generalized Runge-Kutta method GRK [22], the analytical inversion method AIM [23], the piecewise constant approximation PCA [24], the numerical algorithm CORE [25], the better basis function BBF, Hermit polynomial methods [26], the generalized analytical exponential method, GAEM and Pade' approximation with treatment of inhour equation root [27], the efficient technique ET [28], the power series method PWS [10], the converged accelerated Taylor series CATS [12], the accurate solution [29], the enhancement of the piecewise constant approximation EPCA [8], the fundamental backward Euler difference scheme BEFD [13], the integral formulation Taylor series expansions ITS2 [2], the Haar wavelet operational method HWOM [30], the modified exponential time differencing ETD [7], the trigonometric Fourier-series solutions TFS [6], and the treatment theta method TTM [31]. Thus, the proposed method is compared with twenty of different numerical methods in Table 3.…”

“…Hamada [4,5] introduced a new method based on Fourier series expansion and then used adaptively step size to solve stiff systems of the PKEs. Nahla [6] used analytical exponential model to solve the stochastic PKEs via eigenvalues and eigenvectors. The modified exponential time differencing method [7] is applied to solve the PKEs.…”

Solución numérica de las ecuaciones estocásticas de la cinética puntual usando el esquema Runge-Kutta implícito de orden 1.5

“…Entre los métodos reportados están: la aproximación constante por partes (PCA) y Monte Carlo (Hayes y Allen, 2005), Euler-Maruyama explícito y Taylor 1.5 (Ray, 2012 ;Ray y Patra, 2013), el método de la cinética puntual estocástica simplificado (SSPK) (Ayyoubzadeh y Vosoughi, 2014), el modelo exponencial analítico (AEM) (Nahla y Edress, 2016a), el modelo estocástico eficiente (ESM) (Nahla y Edress, 2016b), el método de doble diagonalización y descomposición (DDDM) (Da Silva et al, 2016), el método usando lógica difusa (Nayak y Chakraverty, 2016), el método de pasos divididos (Singh y Ray, 2017), el método de Euler-Maryama implícito (Suescún-Díaz et al, 2018), el método de expansión Wiener-Hermite (EWH) (El-Beltagy y Noor, 2019) y finalmente se encuentra el método de validación (Gordon et al, 2021).…”