An inverse problem for computing a leading coefficient in the Sturm–Liouville operator by using the boundary data

Hasanov, 1997, Solution of an inverse coefficient problem for an ordinary differential equation, Appl. Anal., 67, 11, 10.1080/00036819708840594 Kaltenbacher, 2000, A projection-regularized Newton method for nonlinear ill-posed problems and its application to parameter identification problems with finite element discretization, SIAM J. Numer. Anal., 37, 1885, 10.1137/S0036142998347322 Hasanov, 2002, Simulation of ill-conditioned situations in inverse coefficient problem for the Sturm–Liouville operator based on boundary measurements, Math. Comput. Simul., 61, 47, 10.1016/S0378-4754(02)00134-9 Seyidmamedov, 2002, Determination of leading coefficients in Sturm–Liouville operator from boundary measurements. I. A stripping algorithm, Appl. Math. Comput., 125, 1, 10.1016/S0096-3003(00)00104-1 Hasanov, 2002, Determination of leading coefficients in Sturm–Liouville operator from boundary measurements. II. Unicity and an engineering approach, Appl. Math. Comput., 125, 23, 10.1016/S0096-3003(00)00105-3 Liu, 2008, Solving an inverse Sturm–Liouville problem by a Lie-group method, Boundary Value Probl., 10.1155/2008/749865 Liu, 2008, A novel fictitious time integration method for solving the discretized inverse Sturm–Liouville for specified eigenvalues problems, CMES: Comput. Model. Eng. Sci., 36, 261 Hasanov, 2003, An inverse polynomial method for the identification of the leading coefficient in the Sturm–Liouville operator from boundary measurements, Appl. Math. Comput., 140, 501, 10.1016/S0096-3003(02)00248-5 Yeung, 1996, Second-order finite difference approximation for inverse determination of thermal conductivity, Int. J. Heat Mass Transf., 39, 3685, 10.1016/0017-9310(96)00028-2 Keung, 1998, Numerical identifications of parameters in parabolic systems, Inv. Prob., 14, 83, 10.1088/0266-5611/14/1/009 Lin, 2001, Inverse method for estimating thermal conductivity in one-dimensional heat conduction problems, J. Thermophys. Heat Transf., 15, 34, 10.2514/2.6593 Chang, 2006, Non-iteration estimation of thermal conductivity using finite volume method, Int. Commun. Heat Mass Transf., 33, 1013, 10.1016/j.icheatmasstransfer.2006.02.010 Jia, 2004, Identifications of parameters in ill-posed linear parabolic equations, Nonlinear Anal., 57, 677, 10.1016/j.na.2004.03.011 Liu, 2007, Highly accurate computation of spatial-dependent heat conductivity and heat capacity in inverse thermal problem, CMES: Comput. Model. Eng. Sci., 17, 1 Liu, 2008, An LGSM to identify nonhomogeneous heat conductivity functions by an extra measurement of temperature, Int. J. Heat Mass Transf., 51, 2603, 10.1016/j.ijheatmasstransfer.2008.01.010 Lam, 1995, Inverse determination of thermal conductivity for one-dimensional problems, J. Thermophys. Heat Transf., 9, 335, 10.2514/3.665 Chen, 2006, Solving an inverse parabolic problem by optimization from final measurement data, J. Comput. Appl. Math., 193, 183, 10.1016/j.cam.2005.06.003 Tadi, 1997, Inverse heat conduction based on boundary measurement, Inv. Prob., 13, 1585, 10.1088/0266-5611/13/6/012 Engl, 2000, A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction, Inv. Prob., 16, 1907, 10.1088/0266-5611/16/6/319 Ito, 1990, The augmented Lagrangian method for parameter estimation in elliptic systems, SIAM J. Contr. Optim., 28, 113, 10.1137/0328006 Ito, 1996, Augmented Lagrangian-SQR-methods in Hilbert spaces and applications to control in the coefficients problems, SIAM J. Optim., 6, 96, 10.1137/0806007 Ben-yu, 2001, An augmented Lagrangian method for parameter identifications in parabolic systems, J. Math. Anal. Appl., 263, 49, 10.1006/jmaa.2001.7593 Chen, 1999, An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems, SIAM J. Contr. Optim., 37, 892, 10.1137/S0363012997318602 Liu, 2006, The Lie-group shooting method for nonlinear two-point boundary value problems exhibiting multiple solutions, CMES: Comput. Model. Eng. Sci., 13, 149 Liu, 2006, Efficient shooting methods for the second order ordinary differential equations, CMES: Comput. Model. Eng. Sci., 15, 69 Liu, 2006, The Lie-group shooting method for singularly perturbed two-point boundary value problems, CMES: Comput. Model. Eng. Sci., 15, 179 Liu, 2001, Cone of non-linear dynamical system and group preserving schemes, Int. J. Non-Linear Mech., 36, 1047, 10.1016/S0020-7462(00)00069-X Liu, 2006, One-step GPS for the estimation of temperature-dependent thermal conductivity, Int. J. Heat Mass Transf., 49, 3084, 10.1016/j.ijheatmasstransfer.2005.11.036 Liu, 2006, An efficient simultaneous estimation of temperature-dependent thermophysical properties, CMES: Comput. Model. Eng. Sci., 14, 77 Liu, 2007, Identification of temperature-dependent thermophysical properties in a partial differential equation subject to extra final measurement data, Numer. Methods Partial Diff. Eq., 23, 1083, 10.1002/num.20211 Liu, 2010, An iterative and adaptive Lie-group method for solving the Calderón inverse problem, CMES: Comput. Model. Eng. Sci., 64, 299 Liu, 2010, A Lie-group adaptive method for imaging a space-dependent rigidity coefficient in an inverse scattering problem of wave propagation, CMC: Comput. Mater. Cont., 18, 1 Liu, 2011, A self-adaptive LGSM to recover initial condition or heat source of one-dimensional heat conduction equation by using only minimal boundary thermal data, Int. J. Heat Mass Transf., 54, 1305, 10.1016/j.ijheatmasstransfer.2010.12.013 Liu, 2011, Using a Lie-group adaptive method for the identification of a nonhomogeneous conductivity function and unknown boundary data, CMC: Comput. Mater. Cont., 21, 17 Liu, 2011, A Lie-group adaptive method to identify spatial-dependence heat conductivity coefficients, Numer. Heat Transf. Part B, 60, 305, 10.1080/10407790.2011.609103 Keung, 2000, An efficient linear solver for nonlinear parameter identification problems, SIAM J. Sci. Comput., 22, 1511, 10.1137/S1064827598346740 Cao, 2010, Regularization of naturally linearized parameter identification problems and the application of the balancing principle, 65 Liu, 2009, A highly accurate technique for interpolations using very high-order polynomials, and its applications to some ill-posed linear problems, CMES: Comput. Model. Eng. Sci., 43, 253