Numerical Initial Value Problems in Ordinary Differential Equations

This is cne of the r-are text books written in the discipline of Nuclear Reactor Analysis, where the author has considered the interests of both scientists and practising engineers, in addition to serving the needs of the academia. The most attractive feature of this book is a balanced treatment of theory and practice of the subject matter. The theoretical foundations of the reactor design methods are explained with simplified definitions and relevant practical illustrations. The author scans through quickly the traditional aspects of the so-called reactor physics and takes the reader through the details of the analytical aspects in a conventional manner. Hcwever, there is a definite departure from the classical method of approach in order to avoid lengthy and repetitive discussions, that are available in many standard text books on reactor physics. The chief departure fran tradition is the priority accorded to the treatment of the energy part of the problems as opposed to the spatial Dart normally devoted to by other authors . A similar unorthodox approach has been applied while dealing with the solution of the various equations by giving priority to computer oriented mrethods as opposed to the classical solutions.

Nuclear reactor analysis

Fractional neutron point kinetics equations for nuclear reactor dynamics

A numerical procedure to efficiently calculate the solution to the point kinetics equation in nuclear reactor dynamics is described and investigated. Piecewise constant approximations of the reactivity and source functions are made. The resulting system of linear differential equations is solved exactly over each time step. The method is proved to converge with order h2 where h is the time step. The procedure is tested using a variety of initial conditions, data, and reactivity functions. The computational results indicate that the method is efficient and accurate.

Efficient numerical solution of the point kinetics equation

Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics

A method based on the Pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity. The technique consists of treating explicitly the roots of the inhour formula. A significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation, which usually would make the Pade approximation inaccurate. Also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the Pade approximations. Results are presented for several cases of Pade approximations using various options of the method with different types of reactivity. The formalism is applicable equally well to non-linear problems, where the reactivity depends on the neutron density through temperature feedback. It was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases.

http://iopscience.iop.org/article/10.1088/0305-4470/35/45/309/pdf

Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Padé approximations via the analytical inversion method

A method based on the analytical inversion of polynomials of the point kinetics matrix is applied to the solution of the reactor kinetics equations. This method permits a fast inversion of polynomials by going temporarily to the complex plane. Several cases using various options of the method are presented for comparison. The method developed was found to be very fast and accurate, and has the ability to reproduce all the features of transients, including prompt jump. The analysis of the assumption of constant parameters, reactivity, and source, during a time step, are included. It is concluded that the method provides a fast and accurate computational technique for the point kinetics equations with step reactivity.

Ahmed E. Aboanber

Papers

Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Padé approximations via the analytical inversion method

Generalization of the analytical inversion method for the solution of the point kinetics equations

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

PWS: an efficient code system for solving space-independent nuclear reactor dynamics

On pade′ approximations to the exponential function and application to the point kinetics equations