References
- R. J. R. Hughes , Unconditionally Stable Algorithms for Nonlinear Heat Conduction , Comput. Meth. Appl. Mech. Eng. , vol. 10 , pp. 135 – 139 , 1977 .
- S. Orivuori , Efficient Method for Solution of Nonlinear Heat Conduction Problems , Int. J. Numer. Meth. Eng. , vol. 14 , pp. 1461 – 1476 , 1979 .
- J. Kujawski , Collocation Time Finite Element Procedures for Integration of Strongly Nonlinear Initial Value Problems , Int. J. Numer. Meth. Eng. , vol. 23 , pp. 579 – 589 , 1986 .
- W. F. Ames , Numerical Methods for Partial Differential Equations, , 3d ed. , pp. 102 – 105 , Academic Press , London , 1992 .
- A. S. Franca and K. Haghighi , Adaptive Finite Element Analysis of Transient Thermal Problems , Numer. Heat Transfer B, F , vol. 26 , pp. 273 – 292 , 1994 .
- K. W. Morton and D. F. Mayers , Numerical Solution of Partial Differential Equations: An Introduction , pp. 52 – 53 , Cambridge University Press , New York , 1994 .
- M. Lobo and A. Emery , Use of the Discrete Maximum Principle in Finite-Element Analysis of Combined Conduction and Radiation in Nonparticipating Media , Numer. Heat Transpfer B, F , vol. 27 , pp. 447 – 465 , 1995 .
- D. Lesnic , L. Elliott , and D. B. Ingham , Identification of the Thermal Conductivity and Heat Capacity in Unsteady Nonlinear Heat Conduction Problems Using the Boundary Element Method , J. Comput. Phys. , vol. 126 , pp. 410 – 420 , 1996 .
- M. Krizek and L. Liu , Finite Element Approximation of a Nonlinear Heat Conduction Problem in Anisotropic Media , Comput. Meth. Appl. Mech. Eng. , vol. 157 , pp. 387 – 397 , 1998 .
- J. Ockendon , Applied Partial Differential Equations , pp. 260 – 266 , Oxford University Press , New York , 1999 .
- S.-J. Liao and A. T. Chwang , General Boundary-Element Method for Unsteady Nonlinear Heat Transfer Problems, Numer. Heat Transfer B, F , vol. 35, pp. 225–242, 1999.
- J. Blobner , R. A. Biaecki , and G. Kunh , Boundary-Element Solution of Coupled Heat Conduction-Radiation Problems in the Presence of Shadow Zones , Numer. Heat Transfer B, F , vol. 39 , pp. 451 – 478 , 2001 .
- B. Chen , Y. Gu , Z. Guan , and H. Zhang , Nonlinear Transient Heat Conduction Analysis with Precise Time Integration Method , Numer. Heat Transfer B, F , vol. 40 , pp. 325 – 341 , 2001 .
- F. Asllanaj , A. Milandri , G. Jeandel , and J. R. Roche , A Finite Difference Solution of Non-linear Systems of Radiative-Conductive Heat Transfer Equations , Int. J. Numer. Meth. Eng. , vol. 54 , pp. 1649 – 1668 , 2002 .
- A. Fic , R. A. Bialecki , and A. J. Kassab , Solving Transient Nonlinear Heat Conduction Problems by Proper Orthogonal Decomposition and the Finite-Element Method , Numer. Heat Transfer B, F , vol. 48 , pp. 103 – 124 , 2005 .
- M. M. Gupta , L. Jin , and N. Homma , Static and Dynamic Neural Networks , pp. 345 – 354 , Wiley , NewYork , 2003 .
- J. J. Hopfield , Neurons with Graded Response Have Collective Computational Properties Like Those of Two-State Neurons , Proc. Nat. Acad. Science USA , vol. 81 , pp. 3088 – 3092 , 1984 .
- J. J. Hopfield and D. W. Tank , Computing with Neural Circuits: A Model , Science , vol. 233 , pp. 625 – 633 , 1986 .
- G. Fei , Z. Peng , W. Fang , M. Xikni , and Q. Guanyuan , Finite Element Analysis Based Hopfield Neural Network Model for Solving Nonlinear Electromagnetic Field Problems , Neural Networks, IJCNN '99 Int. Joint Conf. on , 1999 , Washington , DC , vol. 6 , pp. 4399 – 4403 .
- S. Deng and Y. Hwang , Applying Neural Networks to the Solution of Forward and Inverse Heat Conduction Problems , Int. J. Heat and Mass Transfer , vol. 49 , pp. 4732 – 4750 , 2006 .
- R. D. Richtmyer and K. W. Morton , Difference Methods for Initial Value Problems, , 2d ed. , pp. 201 – 206 , Wiley , New York , 1967 .
- P. C. Tuan , C. C. Ji , L. W. Fong , and W. T. Huang , Application of Kalman Filtering with Input Estimation Technique to On-line Cylindrical Inverse Heat Conduction Problems , Int. J. Jpn. Soc. Mech. Eng. Ser. B , vol. 40 , pp. 126 – 133 , 1997 .
- G. D. Smith , Numerical Solution of Partial Differential Equations: Finite Difference Methods, , 3d ed. , pp. 146 – 148 , Clarendon Press , Oxford and New York , 1985 .
- A. A. Samarski , V. A. Galaktionov , S. P. Kurdyumov , and A. P. Mikhailov , Blow-up in Quasilinear Parabolic Equations , pp. 14 – 18 , de Gruyter Expositions in Mathematics, de Gruyter, Berlin and Hawthorne , NY , 1995 .
- A. Munier , J. Burgan , J. Gutierrez , E. Fijalkow , and M. R. Feix , Group Transformations and the Nonlinear Heat Diffusion Equation , SIAM J. Appl. Math. , vol. 40 , pp. 191 – 207 , 1981 .