Geodesic
A matrix constructive method for the analytic-numerical solution of coupled partial differential systems
Applications of Mathematics, Tome 40 (1995) no. 5, pp. 391-400.

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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.
DOI : 10.21136/AM.1995.134302
Classification : 15A24, 15A45, 15A60, 35K15, 65F15, 65M70, 65N15
Keywords: Schur decomposition; partial differential system; eigenvalues bound; matrix norms; analytic-numerical solution; error bounds 
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Jódar, Lucas; Navarro, Enrique; Ferrer, M. V. A matrix constructive method for the analytic-numerical solution of coupled partial differential systems. Applications of Mathematics, Tome 40 (1995) no. 5, pp. 391-400. doi : 10.21136/AM.1995.134302. http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134302/

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