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This article deals with one-dimension backward heat conduction problem (BHCP). A new approach based on least squares support vector machines (LS-SVM) is proposed for obtaining their approximate solutions. The approximate solution is presented in closed form by means of LS-SVM, whose parameters are adjusted to minimize an appropriate error function. The approximate solution consists of two parts. The first part is a known function that satisfies initial and boundary conditions. The other is a product of two terms. One term is known function which has zero boundary and initial conditions, another term is unknown which is related to kernel functions. This method has been successfully tested on practical examples and has yielded higher accuracy and stable solutions.
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참고문헌 (16)
참고문헌 신청
O. M. Alifanov / 1994 / Inverse Hear Transfer Problems. International series in heat and mass transfer / Spingger-Verlag
Ghosh / 2011 / Inverse estimation of lo-cation of internal heat source in conduction / Inverse problem in science and engineering 19(3):337~361
X. T. Xiong / 2010 / A numerical method for identifying heat transfer coefficient / Applied Mathematical Modelling 34:1930~1938
C. W. Chang / 2010 / A backward group preserving scheme for multi-dimensional backward heat conduction problems / CMES, Tech Science Press 59(3):239~274
D. Colton / 1979 / The approximation of solutions to the backwards heat equation in a nonhomogeneous medium / J. Math. Anal. Appl 72:419~429
Ghosh / 2011 / Inverse estimation of lo-cation of internal heat source in conduction / Inverse problem in science and engineering 19(3):337~361
X. T. Xiong / 2010 / A numerical method for identifying heat transfer coefficient / Applied Mathematical Modelling 34:1930~1938
C. W. Chang / 2010 / A backward group preserving scheme for multi-dimensional backward heat conduction problems / CMES, Tech Science Press 59(3):239~274
D. Colton / 1979 / The approximation of solutions to the backwards heat equation in a nonhomogeneous medium / J. Math. Anal. Appl 72:419~429
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