Article
MSC:
15A24,
15A45,
15A60,
35K15,
65F15,
65M70,
65N15 | MR 1342368 | Zbl 0841.65087 | DOI: 10.21136/AM.1995.134302
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Keywords:
Schur decomposition; partial differential system; eigenvalues bound; matrix norms; analytic-numerical solution; error bounds
Schur decomposition; partial differential system; eigenvalues bound; matrix norms; analytic-numerical solution; error bounds
Summary:
In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation $u_t-Au_{xx}-Bu=0$, where $B$ is an arbitrary square complex matrix and $A$ ia s matrix such that the real part of the eigenvalues of the matrix $\frac{1}{2}(A+A^H)$ is positive. Given an admissible error $\varepsilon $ and a finite domain $G$, and analytic-numerical solution whose error is uniformly upper bounded by $\varepsilon $ in $G$, is constructed.
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