Product integration for the linear transport equation in slab geometry (Q1822476)

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 is \(O(n^{-3+\delta})\), \(\delta >0\) 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.