Power series solution (PWS) of nuclear reactor dynamics with newtonian temperature feedback

Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method

“…Substituting (27) into (25) and (17) can get ( ) and ( ); then the neutron density (or power) will be obtained by (8).…”

“…The PWR with fuel 235 U is taken as an example with parameters = 0.0065, = 0.0001 s, = 0.0774 1/s, = 0.05 K/MW⋅s, and = 5 × 10 −5 1/K [8,13]. For the reactor with the initial power 1 MW, while reactivity 0 = 0.5 and 0 = 0.8333 is inserted, respectively, the variations of reactivity, temperature, power with time, and power with reactivity are presented in Figures 1, 2, 3 very small step size [17].…”

“…The analysis of variation of neutron density (or power) and reactivity with time under the different conditions is an important content of nuclear reactor physics or neutron kinetics [1][2][3][4][5][6][7]. Some important achievements on the supercritical transient with temperature feedback with big ( 0 > ) or small ( 0 < ) reactivity inserted have been approached through the effort of many scholars [7][8][9][10][11][12]. The studies on the delayed supercritical transient with small reactivity inserted and temperature feedback are introduced in the related literature [13][14][15], in which the explicit function of density (or power) and reactivity with respect to time is derived mainly with decoupling method, power prompt jump approximation, precursor prompt jump approximation, temperature prompt jump approximation [10,16], and so forth.…”

Explicit appropriate basis function method for numerical solution of stiff systems

“…And there are several methods especially adapted for solving the initial value problems for stiff systems of ordinary differential equations (Aboanber and Hamada, 2003;Aboanber, 2004;Tashakor et al, 2010). Among the methods are numerical integration using Simpson's rule, finite element method, Runge-Kutta procedures, quasi-static method, piecewise polynomial approach and other methods (Li et al, 2010;Abdallah and Nahla, 2011;Hamada, 2013).…”

An accurate solution of point kinetics equations of one-group delayed neutrons and an extraneous neutron source for step reactivity insertion

“…A small step results in a long computing time, and more importantly, there is large accumulated error due to *These authors contributed equally to this work †Corresponding author (email: Cwz2@21cn.com) the many computation steps. Many researchers have attempted to solve this problem and some relatively effective numerical methods have been proposed, such as the finite-difference method [5], finite-element method [6], Runge-Kutta procedure [7], quasistatic method [8,9], piecewise polynomial approach [10], singular perturbation method [11], stiffness confinement method [12], power series solution [13][14][15], and Padé approximation [16][17][18].…”