Berrut, Jean-Paul Mittelmann, Hans D. 2004-11-30 Due to their rapid – often exponential – convergence as the number N of interpolation/collocation points is increased, polynomial pseudospectral methods are very efficient in solving smooth boundary value problems. However, when the solution displays boundary layers and/or interior fronts, this fast convergence will merely occur with very large N. To address this difficulty, we present a method which replaces the polynomial ansatz with a rational function r and considers the physical domain as the conformal map g of a computational domain. g shifts the interpolation points from their classical position in the computational domain to a problem-dependent position in the physical domain. Starting from a map by Bayliss and Turkel we have constructed a shift that can in principle accomodate an arbitrary number of fronts. Its parameters as well as the poles of r are optimized. Numerical results demonstrate how g best accomodates interior fronts while the poles also handle boundary layers. application/pdf https://folia.unifr.ch/global/documents/299656 https://folia.unifr.ch/documents/299656/files/1_berrut_ops.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcp.2004.10.009 info:eu-repo/semantics/openAccess License undefined Journal of Computational Physics. - 2005, vol. 204, no. 1, p. 292-301 two-point boundary value problems linear rational collocation pole optimization mesh generation point shift optimization info:eu-repo/classification/udc/51 Optimized point shifts and poles in the linear rational pseudospectral method for boundary value problems http://purl.org/coar/resource_type/c_6501