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.
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Monegato, G., Colombo, V. Product integration for the linear transport equation in slab geometry. Numer. Math. 52, 219–240 (1988). https://doi.org/10.1007/BF01398690
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DOI: https://doi.org/10.1007/BF01398690