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Volumn 53, Issue 19-20, 2010, Pages 4132-4140

A highly accurate LGSM for severely ill-posed BHCP under a large noise on the final time data

Author keywords

Backward heat conduction problem; Inverse problem; Lie group shooting method; Noisy data; Strongly ill posed problem

Indexed keywords

BACKWARD HEAT CONDUCTION PROBLEM; HEAT CONDUCTION PROBLEMS; ILL POSED PROBLEM; LIE-GROUP SHOOTING METHOD; NOISY DATA;

EID: 77954535504     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2010.05.036     Document Type: Article
Times cited : (31)

References (32)
  • 1
    • 0035480574 scopus 로고    scopus 로고
    • Cone of non-linear dynamical system and group preserving schemes
    • Liu C.-S. Cone of non-linear dynamical system and group preserving schemes. Int. J. Non-Linear Mech. 2001, 36:1047-1068.
    • (2001) Int. J. Non-Linear Mech. , vol.36 , pp. 1047-1068
    • Liu, C.-S.1
  • 2
    • 27644553495 scopus 로고    scopus 로고
    • Nonstandard group-preserving schemes for very stiff ordinary differential equations
    • Liu C.-S. Nonstandard group-preserving schemes for very stiff ordinary differential equations. CMES: Comput. Model. Eng. Sci. 2005, 9:255-272.
    • (2005) CMES: Comput. Model. Eng. Sci. , vol.9 , pp. 255-272
    • Liu, C.-S.1
  • 3
    • 33646784731 scopus 로고    scopus 로고
    • Preserving constraints of differential equations by numerical methods based on integrating factors
    • Liu C.-S. Preserving constraints of differential equations by numerical methods based on integrating factors. CMES: Comput. Model. Eng. Sci. 2006, 12:83-107.
    • (2006) CMES: Comput. Model. Eng. Sci. , vol.12 , pp. 83-107
    • Liu, C.-S.1
  • 4
    • 12344271462 scopus 로고    scopus 로고
    • The method of fundamental solutions for the backward heat conduction problem
    • Mera N.S. The method of fundamental solutions for the backward heat conduction problem. Inv. Probl. Sci. Eng. 2005, 13:65-78.
    • (2005) Inv. Probl. Sci. Eng. , vol.13 , pp. 65-78
    • Mera, N.S.1
  • 5
    • 1842534840 scopus 로고    scopus 로고
    • Group preserving scheme for backward heat conduction problems
    • Liu C.-S. Group preserving scheme for backward heat conduction problems. Int. J. Heat Mass. Transfer 2004, 47:2567-2576.
    • (2004) Int. J. Heat Mass. Transfer , vol.47 , pp. 2567-2576
    • Liu, C.-S.1
  • 6
    • 33646850601 scopus 로고    scopus 로고
    • Past cone dynamics and backward group preserving schemes for backward heat conduction problems
    • Liu C.-S., Chang C.W., Chang J.R. Past cone dynamics and backward group preserving schemes for backward heat conduction problems. CMES: Comput. Model. Eng. Sci. 2006, 12:67-81.
    • (2006) CMES: Comput. Model. Eng. Sci. , vol.12 , pp. 67-81
    • Liu, C.-S.1    Chang, C.W.2    Chang, J.R.3
  • 7
    • 33847712471 scopus 로고    scopus 로고
    • A new shooting method for quasi-boundary regularization of backward heat conduction problems
    • Chang J.R., Liu C.-S., Chang C.W. A new shooting method for quasi-boundary regularization of backward heat conduction problems. Int. J. Heat Mass Transfer 2007, 50:2325-2332.
    • (2007) Int. J. Heat Mass Transfer , vol.50 , pp. 2325-2332
    • Chang, J.R.1    Liu, C.-S.2    Chang, C.W.3
  • 8
    • 67249148129 scopus 로고    scopus 로고
    • A new shooting method for quasi-boundary regularization of multi-dimensional backward heat conduction problems
    • Chang C.W., Liu C.-S., Chang J.R. A new shooting method for quasi-boundary regularization of multi-dimensional backward heat conduction problems. J. Chin. Inst. Eng. 2009, 32:307-318.
    • (2009) J. Chin. Inst. Eng. , vol.32 , pp. 307-318
    • Chang, C.W.1    Liu, C.-S.2    Chang, J.R.3
  • 9
    • 41649113492 scopus 로고    scopus 로고
    • An LGSM to identify nonhomogeneous heat conductivity functions by an extra measurement of temperature
    • Liu C.-S. An LGSM to identify nonhomogeneous heat conductivity functions by an extra measurement of temperature. Int. J. Heat Mass Transfer 2008, 51:2603-2613.
    • (2008) Int. J. Heat Mass Transfer , vol.51 , pp. 2603-2613
    • Liu, C.-S.1
  • 10
    • 46449098515 scopus 로고    scopus 로고
    • An LGEM to identify time-dependent heat conductivity function by an extra measurement of temperature gradient
    • Liu C.-S. An LGEM to identify time-dependent heat conductivity function by an extra measurement of temperature gradient. CMC: Comput., Mater. Continua 2008, 7:81-96.
    • (2008) CMC: Comput., Mater. Continua , vol.7 , pp. 81-96
    • Liu, C.-S.1
  • 11
    • 59049098656 scopus 로고    scopus 로고
    • A two-stage LGSM to identify time-dependent heat source through an internal measurement of temperature
    • Liu C.-S. A two-stage LGSM to identify time-dependent heat source through an internal measurement of temperature. Int. J. Heat Mass Transfer 2009, 52:1635-1642.
    • (2009) Int. J. Heat Mass Transfer , vol.52 , pp. 1635-1642
    • Liu, C.-S.1
  • 12
    • 76249101054 scopus 로고    scopus 로고
    • A three-point BVP of time-dependent inverse heat source problems and solving by a TSLGSM
    • Yeih W., Liu C.-S. A three-point BVP of time-dependent inverse heat source problems and solving by a TSLGSM. CMES: Comput. Model. Eng. Sci. 2006, 46:107-127.
    • (2006) CMES: Comput. Model. Eng. Sci. , vol.46 , pp. 107-127
    • Yeih, W.1    Liu, C.-S.2
  • 13
  • 14
    • 0001293247 scopus 로고
    • The boundary element method for the solution of the backward heat conduction equation
    • Han H., Ingham D.B., Yuan Y. The boundary element method for the solution of the backward heat conduction equation. J. Comp. Phys. 1995, 116:292-299.
    • (1995) J. Comp. Phys. , vol.116 , pp. 292-299
    • Han, H.1    Ingham, D.B.2    Yuan, Y.3
  • 15
    • 0034744604 scopus 로고    scopus 로고
    • An iterative boundary element method for solving the one-dimensional backward heat conduction problem
    • Mera N.S., Elliott L., Ingham D.B., Lesnic D. An iterative boundary element method for solving the one-dimensional backward heat conduction problem. Int. J. Heat Mass Transfer 2001, 44:1937-1946.
    • (2001) Int. J. Heat Mass Transfer , vol.44 , pp. 1937-1946
    • Mera, N.S.1    Elliott, L.2    Ingham, D.B.3    Lesnic, D.4
  • 16
    • 0036749217 scopus 로고    scopus 로고
    • An inversion method with decreasing regularization for the backward heat conduction problem
    • Mera N.S., Elliott L., Ingham D.B. An inversion method with decreasing regularization for the backward heat conduction problem. Numer. Heat Transfer B 2002, 42:215-230.
    • (2002) Numer. Heat Transfer B , vol.42 , pp. 215-230
    • Mera, N.S.1    Elliott, L.2    Ingham, D.B.3
  • 17
    • 0033096606 scopus 로고    scopus 로고
    • A comparison of some inverse methods for estimating the initial condition of the heat equation
    • Muniz W.B., de Campos Velho H.F., Ramos F.M. A comparison of some inverse methods for estimating the initial condition of the heat equation. J. Comp. Appl. Math. 1999, 103:145-163.
    • (1999) J. Comp. Appl. Math. , vol.103 , pp. 145-163
    • Muniz, W.B.1    de Campos Velho, H.F.2    Ramos, F.M.3
  • 18
    • 0342520839 scopus 로고    scopus 로고
    • Entropy-and Tikhonov-based regularization techniques applied to the backward heat equation
    • Muniz W.B., Ramos F.M., de Campos Velho H.F. Entropy-and Tikhonov-based regularization techniques applied to the backward heat equation. Int. J. Comp. Math. 2000, 40:1071-1084.
    • (2000) Int. J. Comp. Math. , vol.40 , pp. 1071-1084
    • Muniz, W.B.1    Ramos, F.M.2    de Campos Velho, H.F.3
  • 19
    • 0344514171 scopus 로고    scopus 로고
    • Solution of inverse diffusion problems by operator-splitting methods
    • Kirkup S.M., Wadsworth M. Solution of inverse diffusion problems by operator-splitting methods. Appl. Math. Model. 2002, 26:1003-1018.
    • (2002) Appl. Math. Model. , vol.26 , pp. 1003-1018
    • Kirkup, S.M.1    Wadsworth, M.2
  • 20
    • 3142679353 scopus 로고    scopus 로고
    • Numerical solution of backward heat conduction problems by a high order lattice-free finite difference method
    • Iijima K. Numerical solution of backward heat conduction problems by a high order lattice-free finite difference method. J. Chin. Inst. Eng. 2004, 27:611-620.
    • (2004) J. Chin. Inst. Eng. , vol.27 , pp. 611-620
    • Iijima, K.1
  • 21
    • 33846939256 scopus 로고    scopus 로고
    • A modified method for a backward heat conduction problem
    • Qian Z., Fu C.L., Shi R. A modified method for a backward heat conduction problem. Appl. Math. Comp. 2007, 185:564-573.
    • (2007) Appl. Math. Comp. , vol.185 , pp. 564-573
    • Qian, Z.1    Fu, C.L.2    Shi, R.3
  • 22
    • 33947105490 scopus 로고    scopus 로고
    • Fourier regularization for a backward heat equation
    • Fu C.L., Xiong X.T., Qian Z. Fourier regularization for a backward heat equation. J. Math. Anal. Appl. 2007, 331:472-480.
    • (2007) J. Math. Anal. Appl. , vol.331 , pp. 472-480
    • Fu, C.L.1    Xiong, X.T.2    Qian, Z.3
  • 23
    • 36049002848 scopus 로고    scopus 로고
    • On three spectral regularization methods for a backward heat conduction problem
    • Xiong X.T., Fu C.L., Qian Z. On three spectral regularization methods for a backward heat conduction problem. J. Korean Math. Soc. 2007, 44:1281-1290.
    • (2007) J. Korean Math. Soc. , vol.44 , pp. 1281-1290
    • Xiong, X.T.1    Fu, C.L.2    Qian, Z.3
  • 24
    • 76449101119 scopus 로고    scopus 로고
    • A new method for Fredholm integral equations of 1D backward heat conduction problems
    • Liu C.-S. A new method for Fredholm integral equations of 1D backward heat conduction problems. CMES: Comput. Model. Eng. Sci. 2009, 47:1-21.
    • (2009) CMES: Comput. Model. Eng. Sci. , vol.47 , pp. 1-21
    • Liu, C.-S.1
  • 25
    • 33747359172 scopus 로고    scopus 로고
    • Two numerical methods for solving a backward heat problem
    • Xiong X.T., Fu C.L., Qian Z. Two numerical methods for solving a backward heat problem. Appl. Math. Comp. 2006, 179:374-381.
    • (2006) Appl. Math. Comp. , vol.179 , pp. 374-381
    • Xiong, X.T.1    Fu, C.L.2    Qian, Z.3
  • 26
    • 0242468019 scopus 로고    scopus 로고
    • Different approaches for the solution of a backward heat conduction problem
    • Chiwiacowsky L.D., de Campos Velho H.F. Different approaches for the solution of a backward heat conduction problem. Inv. Probl. Eng. 2003, 11:471-494.
    • (2003) Inv. Probl. Eng. , vol.11 , pp. 471-494
    • Chiwiacowsky, L.D.1    de Campos Velho, H.F.2
  • 27
    • 0007447039 scopus 로고
    • Quasireversibility methods for non-well-posed problems
    • Clark G.W., Oppenheimer S.F. Quasireversibility methods for non-well-posed problems. Elect. J. Diff. Eqns. 1994, 1994:1-9.
    • (1994) Elect. J. Diff. Eqns. , vol.1994 , pp. 1-9
    • Clark, G.W.1    Oppenheimer, S.F.2
  • 29
    • 33744980037 scopus 로고    scopus 로고
    • The Lie-group shooting method for nonlinear two-point boundary value problems exhibiting multiple solutions
    • Liu C.-S. The Lie-group shooting method for nonlinear two-point boundary value problems exhibiting multiple solutions. CMES: Comput. Model. Eng. Sci. 2006, 13:149-163.
    • (2006) CMES: Comput. Model. Eng. Sci. , vol.13 , pp. 149-163
    • Liu, C.-S.1
  • 30
    • 33845426680 scopus 로고    scopus 로고
    • Efficient shooting methods for the second order ordinary differential equations
    • Liu C.-S. Efficient shooting methods for the second order ordinary differential equations. CMES: Comput. Model. Eng. Sci. 2006, 15:69-86.
    • (2006) CMES: Comput. Model. Eng. Sci. , vol.15 , pp. 69-86
    • Liu, C.-S.1
  • 31
    • 33845427623 scopus 로고    scopus 로고
    • The Lie-group shooting method for singularly perturbed two-point boundary value problems
    • Liu C.-S. The Lie-group shooting method for singularly perturbed two-point boundary value problems. CMES: Comput. Model. Eng. Sci. 2006, 15:179-196.
    • (2006) CMES: Comput. Model. Eng. Sci. , vol.15 , pp. 179-196
    • Liu, C.-S.1
  • 32
    • 0000898783 scopus 로고    scopus 로고
    • An iterative boundary element method for solving the backward heat conduction problem using an elliptic approximation
    • Lesnic D., Elliott L., Ingham D.B. An iterative boundary element method for solving the backward heat conduction problem using an elliptic approximation. Inv. Probl. Eng. 1998, 6:255-279.
    • (1998) Inv. Probl. Eng. , vol.6 , pp. 255-279
    • Lesnic, D.1    Elliott, L.2    Ingham, D.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.