Asadzadeh, Mohammad; Kumlin, Peter; Larsson, Stig The discrete ordinates method for the neutron transport equation in an infinite cylindrical domain. (English) Zbl 0767.65095 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) Cited in 5 Documents 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 PDF BibTeX XML Cite \textit{M. Asadzadeh} et al., Math. Models Methods Appl. Sci. 2, No. 3, 317--338 (1992; Zbl 0767.65095) Full Text: DOI