IJPAM: Volume 71, No. 1 (2011)

FINITE DIFFERENCE SCHEMES WHITH EXACT SPECTRUM
FOR SOLVING DIFFERENTIAL EQUATIONS WITH
BOUNDARY CONDITIONS OF THE FIRST KIND

Harijs Kalis$^1$, Sergejs Rogovs$^2$
$^{1,2}$Faculty of Physics and Mathematics
University of Latvia
8, Zellu Iela, Riga, LV 1002, LATVIA


Abstract. In this paper, we introduce the notion of finite difference schemes with exact spectrum (FDSES). We use these shemes for numerical solving ordinary differential equations (ODEs) and partial differential equations (PDEs) with boundary conditions of the first kind. We compare the results obtained by FDSES with the results obtained by other finite difference schemes (FDS). We prove several exact scheme propositions and theorems.

Received: June 29, 2011

AMS Subject Classification: 65F15, 65L10, 65M06, 65M20, 65M22, 65M70

Key Words and Phrases: finite differnces, boundary value problem, initial-boundary value problem, spectral problem

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 1