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Analytic-numerical solutions with a priori error bounds for time-dependent mixed partial differential problems

✍ Scribed by L. Jódar; E. Defez

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
413 KB
Volume
34
Category
Article
ISSN
0898-1221

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✦ Synopsis

The aim of this paper is double. First, we point out that the hypothesis D(tl)D(t2) = D(t2)D(tl) imposed in [1] can be removed. Second, a constructive method for obtaining analyticnumerical solutions with a prefixed accuracy in a bounded domain gl(to, tl) = [0,p] x [t0,tl], for mixed problems of the type ut(x,t) -D(t)uzx(x,t) = 0, 0 < x < p, t > 0, subject to u(O,t) = u(p,t) = 0 and u(z,O) = F(z) is proposed. Here, u(z,t) and F(x) are r-component vectors, D(t) is a C r×r valued analytic function and there exists a positive number 5 such that every eigenvalue z of (1/2) (D(t) + D(t) H) is bigger than 5. An illustrative example is included.

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