References
- Isakov V. Inverse problems for partial differential equations. New York: Springer; 2006.
- Prilepko AI, Orlovsky DG, Vasin IA. Methods for solving inverse problems in mathematical physics. New York: CRC Press, Taylor and Francis Group; 2000.
- Samarskii AA, Vabishchevich PN. Methods for solving inverse problems of mathematical physics. Berlin: Walter de Gruyter; 2007.
- Cannon JR, Van de Hoek J. The one phase Stefan problem subject to energy. J Math Anal Appl. 1982;86(1):281–292.
- Capasso V, Kunisch K. A reaction–diffusion system arising in modelling man-environment diseases. Quart Appl Math. 1988;46:431–450.
- Shidfar A, Karamali GR, Damirchi J. An inverse heat conduction problem with a nonlinear source term. Nonlinear Anal. 2006;65(3):615–621.
- Shidfar A, Damirchi J, Reihani P. An stable numerical algorithm for identifying the solution of an inverse problem. Appl Math Comput. 2007;190(1):231–236.
- Dehghan M. An inverse problem of finding a source parameter in a semilinear parabolic equation. Appl Math Model. 2001;25(9):743–754.
- Lagier G, Lemonnier H, Coutris N. A numerical solution of the linear multidimensional unsteady inverse heat conduction problem with the boundary element method and the singular value decomposition. Int J ThermSci. 2004;43(2):145–155.
- Lesnic D, Elliott L, Ingham DB. An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation. Eng Anal Bound Elem. 1997;20(2):123–133.
- Mera NS, Elliott L, Ingham DB, et al. An iterative boundary element method for the solution of a Cauchy steady state heat conduction problem. Comput Model Eng Sci. 2000;8(6):101–106.
- Wang F, Chen W, Qu W, et al. A BEM formulation in conjunction with parametric equation approach for three-dimensional Cauchy problems of steady heat conduction. Eng Anal Bound Elem. 2016;63:1–14.
- Pourgholi R, Rostamian M. A numerical technique for solving IHCPs using Tikhonov regularization method. Appl Math Modell. 2010;34(8):2102–2110.
- Hon YC, Wei T. A fundamental solution method for inverse heat conduction problem. Eng Anal Bound Elem. 2004;28(5):489–495.
- Lin J, Chen W, Wang F. A new investigation into regularization techniques for the method of fundamental solutions. Math Comput Simul. 2011;81(6):1144–1152.
- Pourgholi R, Dana H, Tabasi SH. Solving an inverse heat conduction problem using genetic algorithm: sequential and multi-core parallelization approach. Appl Math Modell. 2014;38(7-8):1948–1958.
- Cheng W, Ma YJ, Fu CL. A regularization method for solving the radially symmetric backward heat conduction problem. Appl Math Lett. 2014;30:38–43.
- Liu C-S. A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation. Eng Anal Bound Elem. 2008;32(9):778–785.
- Fu CL, Li HF, Qian Z, et al. Fourier regularization method for solving a Cauchy problem for the Laplace equation. Inverse Probl Sci Eng. 2008;16(2):159–169.
- Liu C-S, Wang F, Gu Y. Trefftz energy method for solving the Cauchy problem of the Laplace equation. Appl Math Lett. 2018;79:187–195.
- Zeybek H, Karakoç SBG. A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline. Springer Plus. 2016;5:199.
- Ak T, Dhawan S, Karakoc SBG, et al. Numerical study of Rosenau-KdV equation using finite element method based on collocation approach. Math Modell Anal. 2017;22:373–388.
- Pavlov VP, Kudoyarova VM. Spline based numerical method for heat conduction nonlinear problems solution. Procedia Eng. 2017;206:704–709.
- Pinkus A. n-widths in approximation theory. Berlin: Springer; 1985.
- De Boor C, Höllig K, Riemenschneider S. Box splines. New York: Springer; 1993.
- De Boor C. A practical guide to splines. Revised ed. New York: Springer-Verlag Inc.; 2000.
- Kunoth A, Lyche T, Sangalli G, et al. Splines and PDEs: from approximation theory to numerical linear algebra. Cetraro: Springer; 2017. (Lecture Notes in Mathematics; vol. 2219).
- Mason JC, Rodriguez G, Seatzu S. Orthogonal splines based on B-splines- with applications to least squares, smoothing and regularization problems. Numer Algorithms. 1993;5(1):25–40.
- Rivlin TJ. An introduction to the approximation of functions. New York: Dover; 1981.
- Hansen PC. Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion. Philadelphia: SIAM; 1998. (Monographs on Mathematical Modeling and Computation.
- Hariharan G, Kannan K, Sharma KR. Haar wavelet method for solving Fisher's equation. Appl Math Comput. 2009;211(2):284–292.
- Tikhonov AN, Arsenin VY. Solutions of ill-posed problems. Washington: Winston and Sons; 1977.
- Wahba G. A survey of some smoothing problems and the method of the generalized cross-validation for solving them. Madison: University of Wisconsin, Department of Statistics; 1976.
- Hansen PC. Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numer Algorithms. 1994;6(1):1–35.
- Byrd RH, Schnabel RB, Shultz GA. A trust region algorithm for nonlinearly constrained optimization. SIAM J Numer Anal. 1987;24(5):1152–1170.
- Rostamian M, Shahrezaee AM. A modified VIM for solving an inverse heat conduction problem. Math Res. 2016;2(1):89–104.
- Pourgholi R, Esfahani A, Foadian S, et al. Resolution of an inverse problem by Haar basis and Legendre wavelet methods. Int J Wavelets, Multiresolution Inf Process. 2013;11(5):1–21.