Numerical solutions with a priori error bounds for coupled self-adjoint time dependent partial differential systems
In: Mathematical and computer modelling, Jg. 29 (1999), Heft 2, S. 1-18
Online
academicJournal
- print, 25 ref
This paper is concerned with the construction of accurate continuous numerical solutions for partial self-adjoint differential systems of the type (P(t) ut)t = Q(t)uxx, u(0, t) = u(d, t) = 0, u(x,0) = f(x), ut(x,0) = g(x), 0 ≤ x ≤ d, t ≥ 0, where P(t), Q(t) are positive definite Rr×r-valued functions such that P'(t) and Q'(t) are simultaneously semidefinite (positive or negative) for all t > 0. First, an exact theoretical series solution of the problem is obtained using a separation of variables technique. After appropriate truncation strategy and the numerical solution of certain matrix differential initial value problems the following question is addressed. Given T > 0 and an admissible error ∈ > 0 how to construct a continuous numerical solution whose error with respect to the exact series solution is smaller than ∈, uniformly in D(T) = {(x, t); 0 ≤ x ≤ d, 0 ≤ t ≤ T}. Uniqueness of solutions is also studied.
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Numerical solutions with a priori error bounds for coupled self-adjoint time dependent partial differential systems
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Autor/in / Beteiligte Person: | PONSODA, E ; JODAR, L |
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Zeitschrift: | Mathematical and computer modelling, Jg. 29 (1999), Heft 2, S. 1-18 |
Veröffentlichung: | Oxford: Elsevier Science, 1999 |
Medientyp: | academicJournal |
Umfang: | print, 25 ref |
ISSN: | 0895-7177 (print) |
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