Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

Approximate methods for solving homogeneous and inhomogeneous boundary-value problems of the nuclear reactor theory are considered. The methods develop the idea of Marchuk's well-known multigroup method [1]. Existence and uniqueness theorems for the corresponding nonlinear equations are proved. A large amount of work has been done on the development and proof of various models of a multigroup and homogenization methods in neutron transport theory, and these problems have to a considerable extend been solved. However, there are some important mathematical questions concerning the choice of particular formulations of problems of this kind, proof of the existence and uniqueness theorems for the solutions of the corresponding linear and non-linear equations, the investigation of the properties of the approximation and the convergence of appropriate numerical techniques for finding them etc, which still appear to be unanswered. In this connection, some multigroup methods for solving homogeneous conditionally critical reactor equations and inhomogeneous neutron transport equations have been examined recently, and the corresponding existence theorems have been established [2,3]. In the present paper we examine, following [2,3], similar aspects concerning existence, uniqueness, and solution techniques for nonlinear equations underlying certain extensions of the Marchuk's multigroup method [1] for homogeneous and inhomogeneous stationary and nonstationary neutron transport theory problems. Existence and uniqueness theorems for the corresponding nonlinear equations are proved.

Note. Abstracts are published in author's edition

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