Convergence Estimates for a Locally One-Dimensional Finite Difference Scheme for Parabolic Initial-Boundary Value Problems

Autor:	C. S. Caldwell
Rok vydání:	1976
Předmět:	Discrete mathematics Numerical Analysis Truncation error Smoothness (probability theory) Differential equation Applied Mathematics Banach space Lambda Combinatorics Computational Mathematics Bounded function Convergence (routing) Boundary value problem Mathematics
Zdroj:	SIAM Journal on Numerical Analysis. 13:514-519
ISSN:	1095-7170 0036-1429
DOI:	10.1137/0713044
Popis:	Error estimates for a locally one-dimensional finite difference scheme for parabolic initial-boundary value problems are presented. Techniques from Bramble, Hubbard and Thomee [1] are applied to a method proposed by Samarskii [5].It is shown that if the right-hand side of the differential equation has “smoothness” $\lambda $ for $1 \leqq \lambda \leqq 2$ and the initial and boundary data have “smoothness” $\mu $ where $0 \leqq \mu \leqq 4$ then the truncation error is bounded by \[ C\left\{ {h^\lambda | f |_{\mathcal{Q}}^{(\lambda )} + h^{{\mu / 2}} | {(\varphi ,{\bf \Phi} )} |_{\mathcal{R} \times \partial \mathcal{Q}}^{(\mu )} } \right\}.\]
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c155077fbb9a3ffc16d9c13b35f61dce https://doi.org/10.1137/0713044 Zobrazit plný text záznamu