The application of modern numerical methods to the neutron transport equation. (English) Zbl 0905.65099
The authors discuss the application of a Galerkin method to a nonlinear evolution equation as well as the construction of the Schwarz algorithm for the neutron transport equation. For the Galerkin approximation the corresponding approximation properties and error estimates are given and in the second case the convergence properties of the algorithm are proved.
Reviewer: W.C.Rheinboldt (Pittsburgh)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35K55 | Nonlinear parabolic equations |
| 82C70 | Transport processes in time-dependent statistical mechanics |
Keywords:
nonlinear Galerkin method; Schwarz algorithm; neutron transport equation; nonlinear evolution equation; error estimates; convergence; algorithmReferences:
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