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Effective approach for the identification of boundary conditions in distributed-parameter systems. (English) Zbl 0637.93019

The author presents two numerical algorithms for solving the problem of identification of boundary values for a parabolic equation. The initial parabolic equation is discretized by using a finite element method in space and orthogonal functions expansion in the time domain. From this discretized problem, the author formulates a discretized problem of identification, by the least squares method with state observations at some interior points. For this problem two specific algorithms are proposed. Numerical examples, for simple 2D problems are presented. The obtained results are in a good accordance with the exact results.
Reviewer: Chr.Saguez

MSC:

93B30 System identification
93B40 Computational methods in systems theory (MSC2010)
93C20 Control/observation systems governed by partial differential equations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
35K20 Initial-boundary value problems for second-order parabolic equations
35R30 Inverse problems for PDEs
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

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