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Semianalytic Solution of Boundary Value Problems by Using Approximated Operators
Author(s) -
Gartland E. C.,
Grossmann C.
Publication year - 1992
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19920721202
Subject(s) - piecewise , discretization , mathematics , convergence (economics) , operator (biology) , simple (philosophy) , boundary value problem , differential operator , taylor series , mathematical analysis , biochemistry , chemistry , philosophy , epistemology , repressor , transcription factor , economics , gene , economic growth
Adapted discretization methods can be obtained by a piecewise simplification of the differential operator and by exactly solving of the generated auxiliary problems. In the present paper we introduce a simple convergence analysis which rests on perturbed operators. Using special constructions of the perturbations the convergence of methods being based on piecewise truncated Taylor's expansions can be established. These methods are closely related to compact difference schemes.