The discrete ordinates method for the neutron transport equation in an infinite cylindrical domain. (English) Zbl 0767.65095

Asadzadeh, Mohammad; Kumlin, Peter; Larsson, Stig

Math. Models Methods Appl. Sci. 2, No. 3, 317-338 (1992).

Regularity results proven for a Fredholm integral equation with weakly singular kernel connected with a one-velocity neutron transport equation in an infinite cylinder are used to derive error estimates in \(L_ 1\)- norm for the discrete ordinates method to solve the neutron transport problem. An error bound for the critical eigenvalue of the corresponding problem is obtained as a consequence. The regularity is established using Besov space techniques.

Reviewer: L.P.Lebedev (Rostov-na-Donu)

MSC:

65R20	Numerical methods for integral equations
45K05	Integro-partial differential equations
82C70	Transport processes in time-dependent statistical mechanics
45C05	Eigenvalue problems for integral equations

Keywords:

cylindrical domain; convergence; regularity; error bound; Fredholm integral equation; weakly singular kernel; neutron transport equation; error estimates; discrete ordinates method; critical eigenvalue; Besov space techniques