Determination of a time-dependent parameter in a one-dimensional quasi-linear parabolic equation with temperature overspecification

References

• Cannon , J. R. and Lin , Y. 1988 . Determination of parameter p(t) in Holder classes for some semilinear parabolic equations . Inverse Problems , 4 : 595 – 606 .
   Web of Science ®Google Scholar
• Cannon , J. R. and Lin , Y. 1990 . Numerical solutions of some parabolic inverse problems . Numerical Methods for Partial Differential Equations , 2 : 177 – 191 .
   Google Scholar
• Cannon , J. R. and Lin , Y. 1990 . An inverse problem of finding a parameter in a semilinear heat equation . Journal of Mathematical Analysis and Applications , 145 : 470 – 484 .
   Web of Science ®Google Scholar
• Cannon , J. R. and Lin , H. M. 1989 . On a class of non-classical parabolic problems . Journal of Differential Equations , 79 : 266 – 288 .
   Web of Science ®Google Scholar
• Cannon , J. R. and Lin , H. M. 1991 . On a class of nonlinear parabolic equations with nonlinear trace type functionals . Inverse Problems , 7 : 149 – 161 .
   Web of Science ®Google Scholar
• Dehghan , M. 2001 . New schemes for a two-dimensional inverse problem with temperature overspecification . Mathematical Problems in Engineering , 7 : 283 – 297 .
   Google Scholar
• Dehghan , M. 2005 . Parameter determination in a partial differential equation from the overspecified data . Mathematical and Computer Modelling , 41 : 196 – 213 .
   Web of Science ®Google Scholar
• Cannon , J. R. , Lin , Y. and Xu , S. 1994 . Numerical procedure for the determination of an unknown coefficient in semilinear parabolic differential equations . Inverse Problems , 10 : 227 – 243 .
   Web of Science ®Google Scholar
• Cannon , J. R. , Lin , Y. and Wang , S. 1992 . Determination of source parameter in parabolic equations . Meccanica , 27 : 85 – 94 .
   Google Scholar
• Dehghan , M. 2002 . Fourth-order techniques for identifying a control parameter in the parabolic equations . International Journal of Engineering Science , 40 : 433 – 447 .
   Web of Science ®Google Scholar
• Dehghan , M. 2003 . Finding a control parameter in one-dimensional parabolic equation . Applied Mathematics and Computation , 135 : 491 – 503 .
   Web of Science ®Google Scholar
• Dehghan , M. 2000 . Finite difference schemes for two-dimensional parabolic inverse problem with temperature overspecification . International Journal of Computer Mathematics , 75 : 339 – 349 .
   Web of Science ®Google Scholar
• Dehghan , M. 2003 . Determination of a control function in three-dimensional parabolic equations . Mathematics and Computers in Simulation , 61 : 89 – 100 .
   Web of Science ®Google Scholar
• Day , W. A. 1982 . Extension of a property of the heat equation to linear thermoelasticity and other theories . Quarterly of Applied Mathematics , 40 : 319 – 330 .
   Web of Science ®Google Scholar
• Adomian , G. 1994 . Solving Frontier Problems of Physics: The Decomposition Method , Boston, MA : Kluwer .
   Google Scholar
• Adomian , G. 1988 . A review of the decompositiom method in applied methematics . Journal of Mathematical Analysis and Applications , 135 : 501 – 544 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. 1999 . A reliable modification of Adomian decomposition method . Applied Mathematics and Computation , 102 : 77 – 86 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. 2000 . A new algorithm for calculating Adomian polynomials for nonlinear operators . Applied Mathematics and Computation , 111 : 53 – 69 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. and Khuri , S. 1996 . A reliable technique for solving the weakly singular second-kind Volterra-type integral equations . Applied Mathematics and Computation , 80 : 287 – 299 .
   Web of Science ®Google Scholar
• Adomian , G. 1991 . Solving frontier problems modeled by nonlinear partial differential equations . Computers & Mathematics with Applications , 22 : 91 – 94 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. and El-Sayed , S. M. 2001 . A new modification of the Adomian decomposition method for linear and nonlinear operators . Applied Mathematics and Computation , 122 : 393 – 405 .
   Web of Science ®Google Scholar
• Dehghan , M. 2004 . The use of Adomian decomposition method for solving the one dimensional parabolic equation with non-local boundary specification . International Journal of Computer Mathematics , 81 : 25 – 34 .
   Web of Science ®Google Scholar
• Lesnic , D. and Elliott , L. 1999 . The decomposition approach to inverse heat conduction . Journal of Mathematical Analysis and Applications , 232 : 82 – 98 .
   Web of Science ®Google Scholar
• Guellal , S. and Cherruault , Y. 1995 . Application of the decomposition method to identify the distributed parameters of an elliptical equation . Mathematical and Computer Modelling , 21 : 51 – 55 .
   Google Scholar
• Dehghan , M. 2004 . The solution of a non-classic problem for one-dimensional hyperbolic equation using the decomposition procedure . International Journal of Computer Mathematics , 81 : 979 – 989 .
   Web of Science ®Google Scholar
• Répaci , A. 1989 . On the solution of a class of inverse evolution problems by Bellman–Adomian method . Applied Mathematics Letters , 2 : 151 – 153 .
   Google Scholar
• Répaci , A. 1989 . Bellman–Adomian solutions of nonlinear inverse problems in continuum physics . Journal of Mathematical Analysis and Applications , 143 : 57 – 65 .
   Web of Science ®Google Scholar
• Babolian , E. , Goghary , S. and Abbasbandy , S. 2005 . Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method . Applied Mathematics and Computation , 161 : 733 – 744 .
   Web of Science ®Google Scholar
• Cherruault , Y. 1990 . Convergence of Adomian’s decomposition method . Mathematical and Computer Modelling , 14 : 83 – 86 .
   Google Scholar
• Cherruault , Y. , Adomian , G. , Abbaoui , K. and Rach , R. 1995 . Further remarks on convergence of decomposition method . International Journal of Bio-Medical Computing , 38 : 89 – 93 .
   PubMedGoogle Scholar
• Cherruault , Y. , Inc , M. and Abbaoui , K. 2002 . On the solution of the nonlinear Korteweg–de Vries equation by the decomposition method . Kybernetes , 31 : 766 – 772 .
   Web of Science ®Google Scholar
• Chrysos , M. , Sanchez , F. and Cherruault , Y. 2002 . Improvement of convergence of Adomian’s method using Padé approximants . Kybernetes , 31 : 884 – 895 .
   Web of Science ®Google Scholar
• Kaya , D. 2000 . An application of the decomposition method for second order wave equations . International Journal of Computer Mathematics , 75 : 235 – 245 .
   Web of Science ®Google Scholar
• Ngarhasta , N. , Some , B. , Abbaoui , K. and Cherruault , Y. 2002 . New numerical study of Adomian method applied to a diffusion model . Kybernetes , 31 : 61 – 75 .
   Web of Science ®Google Scholar
• Dehghan , M. 2006 . Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices . Mathematics and Computers in Simulation , 71 : 16 – 30 .
   Web of Science ®Google Scholar