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-
Acar, R. (1993). Identification of the coefficient in elliptic equations, SIAM J. Control and Optimization. 31, 1221-1244.-
Banks, H. T., and Kunish, K. (1989). Estimation Techniques for Distributed parameter Systems, Birkh¨auser, Boston.-
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.-
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1988). Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin.-
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.-
Don, W. S., and Gottlieb, D. (1994). The Chebyshev–Legendre method: Implementing legendre methods on Chebyshev points, SIAM. J. Numer. Anal. 31, 1519-1534.-
Frind, E. O., and Pinder, G. F. (1973). Galerkin solution of the inverse problem for aquifer transmisitivity, Water Resour. Res. 9, 1397-1410.-
Gottlieb, D., and Orszag, D.(1997). Numerical Analysis of Spectral Methods, Theory and Applications, SIAM-CBMS, SIAM, Philadelphia.-
Guo, B. Y. (1998). Spectral Methods and Their Applications, World Scientific, Singapore.-
Guo B. Y., Cha, K. H., and Kwon, Y. H. (2001). Parameter identification by mixed spectral-pseudospectral approximations, Acta Math. Appl. Sinica. 218-232.-
Nutbrown, D. A. (1975). Identification of parameters in a linear equation of groundwater flow, Water Resour. Res. 11, 581-588.-
Richter, G. R. (1981). An inverse problem for the steady state diffusion equation, SIAM J. Appl. Math. 4, 210-221.-
Richter, G. R. (1981). Numerical identification of a spatially varying diffusion coefficient, Math. Comp. 36, 375-385.-
Vainikko, E., and Kunish, K. (1993). Identifiability of the transmissivity coefficient in an elliptic boundary problem, Z. Anal. Angw. 12, 327-341.-
Vainikko, E., and Vainikko, G. (1992). Some numerical schemes for identification of the filteration coefficient, Acta. Comm. Univ. Tartuensis. 937, 90-102.-
Yeh, W.WG. (1996). Review of parameter identification problems in ground water hydrology: The inverse problem, Water Resour. Res. 22, 95-108-
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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