Perng, Ming-Hwei Effective approach for the identification of boundary conditions in distributed-parameter systems. (English) Zbl 0637.93019 Int. J. Control 45, 607-616 (1987). 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 Cited in 1 Document 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 Keywords:algorithms; identification of boundary values; parabolic equation; finite element method; orthogonal functions expansion PDFBibTeX XMLCite \textit{M.-H. Perng}, Int. J. Control 45, 607--616 (1987; Zbl 0637.93019) Full Text: DOI References: [1] BREBBIA C. A., Boundary Element Techniques in Engineering (1984) · Zbl 0556.73086 [2] DOI: 10.1080/0020718508961135 · Zbl 0555.93014 · doi:10.1080/0020718508961135 [3] DOI: 10.1080/00207177708922326 · Zbl 0405.93012 · doi:10.1080/00207177708922326 [4] DOI: 10.1016/0016-0032(82)90024-2 · Zbl 0502.93032 · doi:10.1016/0016-0032(82)90024-2 [5] DOI: 10.1137/0117057 · Zbl 0185.08204 · doi:10.1137/0117057 [6] DOI: 10.1080/0020718508961177 · Zbl 0562.93021 · doi:10.1080/0020718508961177 [7] DOI: 10.1080/00207178408933305 · Zbl 0551.93018 · doi:10.1080/00207178408933305 [8] DOI: 10.1080/00207178608933577 · Zbl 0586.93026 · doi:10.1080/00207178608933577 [9] SAGARA S., J. Soc. Instrum. Control Engrs 19 pp 1035– (1980) [10] SPARROW E. M., J. appl. Mech. 31 pp 369– (1964) [11] STOLZ G., Trans. ASME, J. Heat Trans. 82 pp 20– (1960) [12] ZIENKIEWICZ O. C., The Finite Element Method (1970) [13] DOI: 10.1002/nme.1620020107 · Zbl 0262.73072 · doi:10.1002/nme.1620020107 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.