The distribution of neutron population in nuclear reactor is described by using transport equations. One of possible approximations of neutron transport equation is given by the neutron diffusion equation. The paper presents numerical solution method of one group neutron diffusion equation with one group of delayed neutrons.

A Newton-Kantorovich convergence theorem of a new modified Halley’s method family is established in a Banach space to solve nonlinear operator equations. We also present the main results to reveal the competence of our method. Finally, two numerical examples arising in the theory of the radiative transfer, neutron transport and in the kinetic theory of gasses are provided to show the applicatio...

The use of an extrapolated-endpoint boundary condition in criticality calculations is discussed from the point of view of two-group neutron-transport theory. The use of a single Milneproblem extrapolated endpoint is justified, from the lowest-order approximation to the transporttheory result, only for certain values of the material properties of a bare multiplying slab.

Nucleon-nucleon momentum correlation function have been presented for nuclear reactions with neutron-rich or proton-rich projectiles using a nuclear transport theory, namely Isospin-Dependent Quantum Molecular Dynamics model. The relationship between the binding energy of projectiles and the strength of proton-neutron correlation function at small relative momentum has been explored, while prot...

Nonlinear quadratic functional integral equations are often applicable for instance in the theory of radiative transfer, kinetic theory of gases, in the theory of neutron transport, in traffic theory and in numerous branches of mathematical physics (cf. [3, 7, 10, 11]). Additionally, some problems (motivated by some practical interests in plasma physics) was investigated in [28]. It is worthwhi...

Transport in very dilute solutions of He-3 in superfluid He-4. Access to the published version may require subscription. Motivated by a proposed experimental search for the electric dipole moment of the neutron (nEDM) utilizing neutron-3 He capture in a dilute solution of 3 He in superfluid 4 He, we derive the transport properties of dilute solutions in the regime where the 3 He are classically...

Integral equations arise naturally in applications of real world problems [5, 6, 7, 8]. The theory of integral equations has been well developed with the help of various tools from functional analysis, topology and fixed-point theory. The classical theory of integral equations can be generalized if one uses the Stieltjes integral with kernels dependent on one or two variables. The aim of this p...