Constructive approximations of mixed variable coefficient diffusion problems
In: Mathematical and computer modelling, Jg. 29 (1999), Heft 6, S. 33-44
Online
academicJournal
- print, 16 ref
This paper deals with the construction of analytical approximations of the problem uxx = (a(x)/b(t))ut, 0 < x < L, t > 0, u(x,0) = f(x), 0 ≤ x ≤ L. First, the uniqueness of solution is studied and an exact series solution is constructed. Given ∈ > 0, 0 < t0 < t1 and D(t0,t1) = {(x,t); 0 < x < L, t0 < t < t1} the truncation index n0 of the series solution is determined in terms of the data so that the error is less than ∈ uniformly in D(t0,t1). Since the truncated series approximation is expressed in terms of exact eigenvalues λ1,..., λn0 and eigen-functions w1(x),..., wn0(x), the admissible errors when one approximates λn by λn and wn(x) by wn(x), 1 < n < n0, are determined so that the global error of an analytical approximation of the problem, constructed in terms of λn, wn(x), 1 ≤ n < n0, is less than ∈ uniformly in D(t0,t1).
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Constructive approximations of mixed variable coefficient diffusion problems
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Autor/in / Beteiligte Person: | ALMENAR, P ; GOBERNA, D ; JODAR, L |
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Zeitschrift: | Mathematical and computer modelling, Jg. 29 (1999), Heft 6, S. 33-44 |
Veröffentlichung: | Oxford: Elsevier Science, 1999 |
Medientyp: | academicJournal |
Umfang: | print, 16 ref |
ISSN: | 0895-7177 (print) |
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