Fin methods of higher order (Q1114364)

The numerical methods proposed here are for diffusion equations on a rectangular domain \(0<x<L\), \(0<y<1\) with L large (modelling a fin). For smooth solutions such problems are nearly 1-dimensional in that the dependence on y is small. In order to take advantage of this behavior, the author introduces a collocation method in the y-direction with a small number of monomials \(y^ n\) as basis functions.