Article

Numerische Mathematik

, Volume 52, Issue 2, pp 219-240

Product integration for the linear transport equation in slab geometry

  • G. MonegatoAffiliated withDipartimento di Matematica, Politecnico di Torino
  • , V. ColomboAffiliated withDipartimento di Energetica, Politecnico di Torino

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Summary

In this paper we present a product quadrature rule for the discretization of the well-known linear transport equation in slab geometry. In particular we give an algorithm for constructing the weights of the rule and prove that the order of convergence isO(n −3+δ ), δ>0 small as we like. Numerical examples are given, and our formula is also compared with product Simpson rules. Finally, we examine a Nyström method based on our quadrature.

Subject Classifications

AMS(MOS):65R20 65D32 CR: G1.4