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

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
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