References
- Fan JT, Cheng X, Wen X. An improved model of heat and moisture transfer with phase change and mobile condensates in fibrous insulation and comparison with experimental results. Int. J. Heat Mass Transfer. 2004;47:2343–2352.
- Li Y, Luo ZX. An improved mathematical simulation of the coupled diffusion of moisture and heat in wool fabrics. Textile Res. J. 1999;69:760–768.
- Xu DH. Mathematical modeling of heat and moisture transfer within textiles and corresponding inverse problems of textile material design. Beijing: Science Press; 2014.
- Xu DH, Chen YB, Zhou XH. Type design for bilayer textile materials under low temperature: modeling, numerical algorithm and simulation. Int. J. Heat Mass Transfer. 2013;60:139–146.
- Xu DH, Ge MB. Thickness determination in textile material design: dynamic modeling and numerical algorithms. Inverse Prob. 2012;28:035011.
- Xu DH, Wen L. An inverse problem of bilayer textile thickness determination in dynamic heat and moisture transfer. Appl. Anal. Int. J. 2013;93:445–465.
- Murio DA. The mollification method and the numerical solution of the inverse heat conduction problem by finite differences. Comput. Math. Appl. 1989;17:1385–1396.
- Murio DA, Guo L. A stable space marching finite differences algorithm for the inverse heat conduction problem with no initial filtering procedure. Inverse Prob. 1990;19:35–50.
- Elden L. Numerical solution of the sideways heat equation by difference approximation in time. Inverse Prob. 1995;11:913–923.
- Hao DN. On a sideways parabolic equation. Inverse Prob. 1997;13:297–309.
- Fu P, Fu CL, Xiong XT, Li HF. Two regularization methods and the order optimal error estimates for a sideways parabolic equation. Comput. Math. Appl. 2005;49:777–788.
- Fu CL, Xiong XT. Fourier regularization method for solving the surface heat flux from interior observations. Math. Comput. Model. 2005;42:489–498.
- Xiong XT, Fu CL, Li HF. Fourier regularization method of a sideways heat equation for determining surface heat flux. J. Math. Anal. Appl. 2006;317:331–348.
- Xiong XT, Fu CL, Cheng J. Spectral regularization methods for solving a sideways parabolic equation within the framework of regularization theory. Math. Comput. Simul. 2009;79:1668–1678.
- Carasso A. Determining surface temperatures from interior observations. SIAM J. Appl. Math. 1982;42:558–574.
- Elden L, Berntsson F, Reginska T. Wavelet and Fourier methods for solving the sideways heat equation. SIAM J. Sci. Comput. 2000;21:2187–2205.
- Seidman T, Elden L. An optimal filtering method for the sideways heat equation. Inverse Prob. 2004;6:681–696.
- Tautenhahn U. Optimal stable approximations for the sideways heat equation. J. Inverse Ill-Posed Prob. 1997;5:287–307.
- Deng YJ, Liu ZH. Iteration methods on sideways parabolic equations. Inverse Prob. 2009;25:095004.
- Hasanov A, Mueller JL. A numerical method for backward parabolic problems with non-selfadjoint elliptic operators. Appl. Numer. Math. 2001;37:55–78.
- Shen XC. Polynomial interpolation I - Lagrange interpolation. Adv. Math. 1983;12:193–214.
- Fornberg B, Zuev J. The Runge phenomenon and spatially variable shape parameters in RBF interpolation. Comput. Math. Appl. 2000;54:379–398.
- Hou ZY, Li HN. The generalized Arcangeli’s method for solving ill-posed problems. Nonlinear Anal. TMA. 1993;21:197–206.
- Yang HQ, Hou ZY. A new regularization method for the operator equation of the first kind. Acta Math. Sin. 1997;40:369–376.
- Elden L. Algorithms for regularization of ill-conditioned least-squares problems. BIT. 1977;17:134–145.
- Hansen PC. Regularization. GSVD and truncated GSVD. BIT. 1989;29:491–504.
- Van Loan CF. Computing the CS and the generalized singular value decomposition. Numer. Math. 1985;46:479–491.