An Iterative Method to Recover the Heat Conductivity Function of a Nonlinear Heat Conduction Equation

REFERENCES

• C.-S. Liu , Using A Lie-Group Adaptive Method for the Identification of a Nonhomogeneous Conductivity Function and Unknown Boundary Data , CMC: Comput., Mater. Continua , vol. 21 , pp. 17 – 39 , 2011 .
   Web of Science ®Google Scholar
• Y. B. Wang , J. Chen , J. Nakagawa , and M. Yamamoto , A Numerical Method for Solving the Inverse Heat Conduction Problem Without Initial Value , Inverse Prob. Sci. Eng. , vol. 18 , pp. 655 – 671 , 2010 .
   Web of Science ®Google Scholar
• W. K. Yeung , and T. T. Lam , Second-Order Finite Difference Approximation for Inverse Determination of Thermal Conductivity , Int. J. Heat Mass Transfer , vol. 39 , pp. 3685 – 3693 , 1996 .
   Web of Science ®Google Scholar
• Y. L. Keung , and J. Zou , Numerical Identifications of Parameters in Parabolic Systems , Inverse Prob. , vol. 14 , pp. 83 – 100 , 1998 .
   Web of Science ®Google Scholar
• Y. L. Keung , and J. Zou , An Efficient Linear Solver for Nonlinear Parameter Identification Problems , SIAM J. Sci. Comput. , vol. 22 , pp. 1511 – 1526 , 2000 .
   Web of Science ®Google Scholar
• J. H. Lin , C. K. Chen , and Y. T. Yang , Inverse Method for Estimating Thermal Conductivity in One-Dimensional Heat Conduction Problems , J. Thermophys. Heat Transfer , vol. 15 , pp. 34 – 41 , 2001 .
   Web of Science ®Google Scholar
• C. L. Chang , and M. Chang , Non-iteration Estimation of Thermal Conductivity Using Finite Volume Method , Int. Comm. Heat Mass Transfer , vol. 33 , pp. 1013 – 1020 , 2006 .
   Web of Science ®Google Scholar
• C. Jia , and G. Wang , Identifications of Parameters in Ill-posed Linear Parabolic Equations , Nonlinear Anal. , vol. 57 , pp. 677 – 686 , 2004 .
   Web of Science ®Google Scholar
• H. W. Engl , and J. Zou , A New Approach to Convergence Rate Analysis of Tikhonov Regularization for Parameter Identification in Heat Conduction , Inverse Prob. , vol. 16 , pp. 1907 – 1923 , 2000 .
   Web of Science ®Google Scholar
• G. Ben-yu , and J. Zou , An Augmented Lagrangian Method for Parameter Identifications in Parabolic Systems , J. Math. Anal. Appl. , vol. 263 , pp. 49 – 68 , 2001 .
   Web of Science ®Google Scholar
• Q. Chen , and J. Liu , Solving an Inverse Parabolic Problem by Optimization from Final Measurement Data , J. Comput. Appl. Math. , vol. 193 , pp. 183 – 203 , 2006 .
   Web of Science ®Google Scholar
• T. T. Lam , and W. K. Yeung , Inverse Determination of Thermal Conductivity for One-Dimensional Problems , J. Thermophys. Heat Transfer , vol. 9 , pp. 335 – 344 , 1995 .
   Web of Science ®Google Scholar
• M. Tadi , Inverse Heat Conduction Based on Boundary Measurement , Inverse Prob. , vol. 13 , pp. 1585 – 1605 , 1997 .
   Web of Science ®Google Scholar
• C.-S. Liu , One-step GPS for The Estimation of Temperature-Dependent Thermal Conductivity , Int. J. Heat Mass Transfer , vol. 49 , pp. 3084 – 3093 , 2006 .
   Web of Science ®Google Scholar
• C.-S. Liu , Cone of Non-Linear Dynamical System and Group Preserving Schemes , Int. J. Non-linear Mech. , vol. 36 , pp. 1047 – 1068 , 2001 .
   Web of Science ®Google Scholar
• C.-S. Liu , An Efficient Simultaneous Estimation of Temperature-Dependent Thermophysical Properties, CMES: Comput. Model. Eng. Sci. , vol. 14, pp. 77–90, 2006.
   Web of Science ®Google Scholar
• C.-S. Liu , Identification of Temperature-Dependent Thermophysical Properties in a Partial Differential Equation Subject to Extra Final Measurement Data , Numer. Meth. Partial Diff. Eq. , vol. 23 , pp. 1083 – 1109 , 2007 .
   Web of Science ®Google Scholar
• C.-S. Liu , L. W. Liu , and H. K. Hong , Highly Accurate Computation of Spatial-Dependent Heat Conductivity and Heat Capacity in Inverse Thermal Problem , CMES: Comput. Model. Eng. Sci. , vol. 17 , pp. 1 – 18 , 2007 .
   Web of Science ®Google Scholar
• C.-S. Liu , and S. N. Atluri , An Iterative and Adaptive Lie-Group Method for Solving the Calderón Inverse Problem , CMES: Comput. Model. Eng. Sci. , vol. 64 , pp. 299 – 326 , 2010 .
   Web of Science ®Google Scholar
• C.-S. Liu , The Lie-Group Shooting Method for Nonlinear Two-Point Boundary Value Problems Exhibiting Multiple Solutions , CMES: Comput. Model. Eng. Sci. , vol. 13 , pp. 149 – 163 , 2006 .
   Web of Science ®Google Scholar
• C.-S. Liu , A Lie-Group Adaptive Method for Imaging a Space-Dependent Rigidity Coefficient in an Inverse Scattering Problem of Wave Propagation , CMC: Comput. Mater. Continua , vol. 18 , pp. 1 – 21 , 2010 .
   Web of Science ®Google Scholar
• C.-S. Liu , 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 Transfer , vol. 54 , pp. 1305 – 1312 , 2011 .
   Web of Science ®Google Scholar
• C.-S. Liu , An LGSM to Identify Nonhomogeneous Heat Conductivity Functions by an Extra Measurement of Temperature , Int. J. Heat Mass Transfer , vol. 51 , pp. 2603 – 2613 , 2008 .
   Web of Science ®Google Scholar
• C.-S. Liu , A Lie-Group Adaptive Method to Identify Spatial-Dependence Heat Conductivity Coefficients . Numer. Heat Transfer B , vol. 60 , pp. 305 – 323 , 2011 .
   Web of Science ®Google Scholar
• A. S. Carraso , Space Marching Difference Schemes in the Nonlinear Inverse Heat Conduction Problem , Inverse Prob. , vol. 8 , pp. 25 – 43 , 1992 .
   Web of Science ®Google Scholar
• L. Elden , Numerical Solution of the Sideways Heat Equation by Difference Approximation in Time , Inverse Prob. , vol. 11 , pp. 913 – 923 , 1995 .
   Web of Science ®Google Scholar
• A. P. Calderón , On an Inverse Boundary Value Problem, Seminar on Numerical Analysis and Its Application to Continuum Physics, Rio de Janeiro, Brazil, Soc. Brasileira de Mathematica , pp 65 – 73 , 1980 .
   Google Scholar
• A. P. Calderón , On an Inverse Boundary Value Problem , Comput. Appl. Math. , vol. 25 , pp. 133 – 138 , 2006 .
   Web of Science ®Google Scholar
• C.-S. Liu , Solving an Inverse Sturm-Liouville Problem by a Lie-Group Method , Bound. Value Prob. , 749865 , 2008 .
   Web of Science ®Google Scholar