Difference Schemes for Nonlinear BVPS on the Semiaxis

Autor:	I.P. Gavrilyuk, M. Hermann, M.V. Kutniv, V.L. Makarov
Rok vydání:	2007
Předmět:	Computational Mathematics Numerical Analysis Applied Mathematics
Zdroj:	Computational Methods in Applied Mathematics. 7:25-47
ISSN:	1609-9389 1609-4840
DOI:	10.2478/cmam-2007-0002
Popis:	The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::19694774c4dd2cb836922d0966c760d0 https://doi.org/10.2478/cmam-2007-0002 Zobrazit plný text záznamu