- Kozlov , V.A. and Maz'ya , V.G. 1990 . On iterative procedures for solving ill-posed boundary value problems that preserve differential equations . Leningrad Math. J. , 5 : 1207 – 1228 .
- Payne , L.E. 1975 . Improperly posed problems in partial differential equations. Regional Conf. Ser. Appl. Math , Philadelphia, PA : SIAM .
- Hadamard , J. 1923 . Lectures on Cauchy Problem in Linear Partial Differential Equations , New Heavens : Yale University Press .
- Miranker , W.L. 1961 . A well posed problem for the backward heat equation . Proc. Amer. Math. Soc. , 12 : 243 – 254 .
- Cannon , J.R. and Douglas , J. Jr. 1967 . The Cauchy problem for the heat equation . SIAM J. Numer. Anal. , 4 : 317 – 327 .
- Cannon , J.R. 1964 . A Cauchy problem for the heat equation . Ann. Mat. Pura. Appl. , 18 : 112 – 114 .
- Han , H. , Ingham , D.B. and Yuan , Y. 1995 . The boundary element method for the solution of the backward heat conduction equation . J Comput. Phys. , 116 : 292 – 299 .
- Lattes , R. and Lions , J.L. 1969 . The Method of Quasi-Reversibility , New York : Amer. Elsevier Publ. .
- Lesnic , D. , Elliott , L. and Ingham , D.B. 1998 . An iterative boundary element method for solving the backward heat conduction problem using an elliptic approximation . Inverse Probl. Eng. , 6 : 255 – 279 .
- Bakushinky , A. and Goncharsky , A. 1994 . Ill-Posed Problems: Theory and Applications , Dordrecht : Kluwer Academic .
- Mera , N.S. , Elliott , L. , L. , Ingham , D.B. and Lesnic , D. 2001 . An iterative boundary element method for solving the one dimensional backward heat conduction problem . Int. J. Heat Mass Transfer , 44 (10) : 1937 – 1946 .
- Jourhmane , M. , Lesnic , D. and Mera , N.S. 2001 . “ Relaxation procedures for an iterative algorithm for solving the Cauchy problem for the Laplace equation (preprint) ” .
- Dautray , R. and Lions , J.L. 1988 . Analyse Matheatique et Calcul Numerique , Paris : Masson .
- Krasnosel'skii , M.A. , Vainikko , G.M. , Zabreiko , P.P. , Rutitskii , Yu.B. and Stetsenko , Yu.V. 1972 . Approximate Solution of Operator Equations , Groningen : Wolters-Noordhoff Publishing .
- Brebbia , C.A. , Telles , J.C.F. and Wrobel , L.C. 1984 . Boundary Element Techniques: Theory and Application in Engineering , Berlin : Springer-Verlag .
- 1991 . NAG Fortran Library Manual , Oxford : The Numerical Algorithms Ltd. . Mark 15.
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An Iterative Algorithm for the Backward Heat Conduction Problem Based on Variable Relaxation Factors
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