Hermite collocation solution of near-singular problems using numerical coordinate transformations based on adaptivity

Autor:	D. M. Sloan, A. W. Lang
Rok vydání:	2002
Předmět:	Moving meshes Hermite spline Collocation Hermite polynomials Applied Mathematics Coordinate system Mathematical analysis Finite difference method Equidistribution Cubic Hermite spline Adaptivity Computational Mathematics Mesh generation Collocation method Hermite collocation Mathematics
Zdroj:	Journal of Computational and Applied Mathematics. 140:499-520
ISSN:	0377-0427
Popis:	A coordinate transformation approach is described that enables Hermite collocation methods to be applied efficiently in one space dimension to steady and unsteady differential problems with steep solutions. The work is an extension of earlier work by Mulholland et al. (J. Comput. Phys. 131 (1997) 280). A coarse grid is generated by an adaptive finite difference method and this grid is used to construct a steady or unsteady coordinate transformation that is based on monotonic cubic spline approximation. An uneven grid is generated by means of the coordinate transformation and the differential problem is solved on this grid using Hermite collocation. Numerical results are presented for steady and unsteady problems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::efb93e48ef442be283696b528894b810 https://doi.org/10.1016/s0377-0427(01)00528-3 Zobrazit plný text záznamu Full Text from ScienceDirect