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Parameter Estimation in Two-Dimensional Space by Mixed Chebyshev–Legendre Approximations

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Abstract

Mixed Chebyshev–Legendre approximations are proposed for identifications of parameters in two-dimensional differential equations. They are easy to be performed, and have the spectral accuracy. Numerical results coincide with theoretical analysis.

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References-

  1. Acar, R. (1993). Identification of the coefficient in elliptic equations, SIAM J. Control and Optimization. 31, 1221-1244.-

    Google Scholar 

  2. Banks, H. T., and Kunish, K. (1989). Estimation Techniques for Distributed parameter Systems, Birkh¨auser, Boston.-

    Google Scholar 

  3. Bernardi, C., and Maday, Y. (1997). Spectral methods. In Ciarlet, P. G., and Lions, J. L. (eds.), Handbook of Numerical Analysis, Vol. 5, Techniques of Scientific Computing, Elsevier, Amsterdam, pp. 209-486.-

    Google Scholar 

  4. Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1988). Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin.-

    Google Scholar 

  5. Cho, C. K., Guo, B. Y., and Kwon, Y. H. (1999). An new approach for numerical identification of conductivity, Appl. Math. & Comp. 100, 265-283.-

    Google Scholar 

  6. Don, W. S., and Gottlieb, D. (1994). The Chebyshev–Legendre method: Implementing legendre methods on Chebyshev points, SIAM. J. Numer. Anal. 31, 1519-1534.-

    Google Scholar 

  7. Frind, E. O., and Pinder, G. F. (1973). Galerkin solution of the inverse problem for aquifer transmisitivity, Water Resour. Res. 9, 1397-1410.-

    Google Scholar 

  8. Gottlieb, D., and Orszag, D.(1997). Numerical Analysis of Spectral Methods, Theory and Applications, SIAM-CBMS, SIAM, Philadelphia.-

    Google Scholar 

  9. Guo, B. Y. (1998). Spectral Methods and Their Applications, World Scientific, Singapore.-

    Google Scholar 

  10. Guo B. Y., Cha, K. H., and Kwon, Y. H. (2001). Parameter identification by mixed spectral-pseudospectral approximations, Acta Math. Appl. Sinica. 218-232.-

  11. Nutbrown, D. A. (1975). Identification of parameters in a linear equation of groundwater flow, Water Resour. Res. 11, 581-588.-

    Google Scholar 

  12. Richter, G. R. (1981). An inverse problem for the steady state diffusion equation, SIAM J. Appl. Math. 4, 210-221.-

    Google Scholar 

  13. Richter, G. R. (1981). Numerical identification of a spatially varying diffusion coefficient, Math. Comp. 36, 375-385.-

    Google Scholar 

  14. Vainikko, E., and Kunish, K. (1993). Identifiability of the transmissivity coefficient in an elliptic boundary problem, Z. Anal. Angw. 12, 327-341.-

    Google Scholar 

  15. Vainikko, E., and Vainikko, G. (1992). Some numerical schemes for identification of the filteration coefficient, Acta. Comm. Univ. Tartuensis. 937, 90-102.-

    Google Scholar 

  16. Yeh, W.WG. (1996). Review of parameter identification problems in ground water hydrology: The inverse problem, Water Resour. Res. 22, 95-108-

    Google Scholar 

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Kwon, Y., Guo, By. & Cha, KH. Parameter Estimation in Two-Dimensional Space by Mixed Chebyshev–Legendre Approximations. Journal of Scientific Computing 18, 235–251 (2003). https://doi.org/10.1023/A:1021116907182

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  • DOI: https://doi.org/10.1023/A:1021116907182

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