Estimation of parameters in partial differential equations from noisy experimental data
作者： John N. Seinfeld , Wen H. Chen
DOI: 10.1016/0009-2509(71)83037-3
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摘要: Abstract The estimation of constant parameters in nonlinear partial differential equations and boundary conditions from noisy experimental data is considered. Nonsequential techniques based on the method steepest descent, quasilinearization, collocation methods are developed. A determining confidence intervals for parameter estimates presented, determination optimal location measurements Examples presented include diffusivity heat equation, activation energy a single reaction dynamic plug flow reactor permeabilities two-region reservoir model.
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sci-hub.se 参考文章(26)
Edward Angel, Inverse boundary-value problems: Elliptic equations Journal of Mathematical Analysis and Applications. ,vol. 30, pp. 86- 98 ,(1970) , 10.1016/0022-247X(70)90185-X
F. W. FAIRMAN‡, D. W. C. SHEN, Parameter identification for a class of distributed systems International Journal of Control. ,vol. 11, pp. 929- 940 ,(1970) , 10.1080/00207177008905973
O. R. Burggraf, An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications Journal of Heat Transfer. ,vol. 86, pp. 373- 380 ,(1964) , 10.1115/1.3688700
J.R. Cannon, B.Frank Jones, Determination of the diffusivity of an anisotropic medium International Journal of Engineering Science. ,vol. 1, pp. 457- 460 ,(1963) , 10.1016/0020-7225(63)90003-X
J.R Cannon, Determination of the unknown coefficient k(u) in the equation ∇ · k(u) ∇u = 0 from overspecified boundary data☆ Journal of Mathematical Analysis and Applications. ,vol. 18, pp. 112- 114 ,(1967) , 10.1016/0022-247X(67)90185-0
A.S. Anderssen, E.T. White, Parameter estimation by the transfer function method Chemical Engineering Science. ,vol. 25, pp. 1015- 1021 ,(1970) , 10.1016/0009-2509(70)85046-1
B. Frank Jones, Various methods for finding unknown coefficients in parabolic differential equations Communications on Pure and Applied Mathematics. ,vol. 16, pp. 33- 44 ,(1963) , 10.1002/CPA.3160160106
J.H. Seinfeld, Identification of parameters in partial differential equations Chemical Engineering Science. ,vol. 24, pp. 65- 74 ,(1969) , 10.1016/0009-2509(69)80009-6
J.R Cannon, Determination of certain parameters in heat conduction problems Journal of Mathematical Analysis and Applications. ,vol. 8, pp. 188- 201 ,(1964) , 10.1016/0022-247X(64)90061-7
James V. Beck, Calculation of Thermal Diffusivity From Temperature Measurements Journal of Heat Transfer. ,vol. 85, pp. 181- 182 ,(1963) , 10.1115/1.3686050