[1] F. S. V. Bazan, M. I. Ismailov and L. Bedin, Time-dependent lowest term estimation in a 2D bioheat transfer problem with nonlocal and convective boundary conditions, Inverse Probl. Sci. Eng. 29 (2021) 1282–1307, https://doi.org/10.1080/17415977.2020.1846034.
[2] M. I. Ismailov, F. S. V. Bazan and L. Bedin, Time-dependent perfusion coefficient estimation in a bioheat transfer problem, Comput. Phys. Commun. 230 (2018) 50–58, https://doi.org/10.1016/j.cpc.2018.04.019.
[3] H. H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol. 1 (1948) 93–122, https://doi.org/10.1152/jappl.1998.85.1.5.
[4] T. C. Shih, T. L. Horng, H. W. Huang, K. C. Ju, T. C. Huang, P. Y. Chen, Y. J. Ho and W. L. Lin, Numerical analysis of coupled effects of pulsatile blood flow and thermal relaxation time during thermal therapy, Int. J. Heat Mass Transf. 55 (2012) 3763–3773, https://doi.org/10.1016/j.ijheatmasstransfer.2012.02.069.
[5] T. C. Shih, P. Yuan, W. L. Lin and H. S. Kou, Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface, Med. Eng. Phys. 29 (2007) 946–953, https://doi.org/10.1016/j.medengphy.2006.10.008.
[6] N. I. Ionkin and V. A. Morozova, The two-dimensional heat equation with nonlocal boundary conditions, Diff. Equat. 36 (2000) 982–987, https://doi.org/10.1007/BF02754498.
[7] W. T. Ang, K. C. Ang and M. Dehghan, The determination of a control parameter in a two-dimensional diffusion equation using a dual-reciprocity boundary element method, Int. J. Comput. Math. 80 (2003) 65–74, https://doi.org/10.1080/00207160304662.
[8] M. Dehghan, Determination of a control parameter in the two-dimensional diffusion equation, Appl. Numer. Math. 37 (2001) 489–502,
https://doi.org/10.1016/S0168- 9274(00)00057-X.
[9] M. Dehghan, An inverse problem of finding a source parameter in a semilinear parabolic equation, Appl. Math. Model. 25 (2001) 743–754,
https://doi.org/10.1016/S0307-904X(01)00010-5.
[10] M. Dehghan and M. Tatari, The radial basis functions method for identifying an unknown parameter in a parabolic equation with overspecified data, Numer. Methods Partial Differential Equations 23 (2007) 984–997, https://doi.org/10.1002/num.20204.
[11] M. I. Ismailov and S. Erkovan, Inverse problem of finding the coefficient of the lowest term in two-dimensional heat equation with Ionkin-type boundary condition, Comput. Math. Math. Phys. 59 (2019) 791–808, https://doi.org/10.1134/S0965542519050087.
[12] M. I. Ismailov, S. Erkovan and A. A. Huseynova, Fourier series analysis of a time-dependent perfusion coefficient determination in a 2D bioheat transfer process, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 38 (2018) 70–78.
[13] M. I. Ismailov, I. Tekin and S. Erkovan, An inverse problem for finding the lowest term of a heat equation with Wentzell-Neumann boundary condition, Inverse Probl. Sci. Eng. 27 (2019) 1608–1634, https://doi.org/10.1080/17415977.2018.1553968.
[14] A. Mohebbi and M. Dehghan, High-order scheme for determination of a control parameter in an inverse problem from the over-specified data, Comput. Phys. Comm. 181 (2010) 1947–1954, https://doi.org/10.1016/j.cpc.2010.09.009.
[15] M. Tatari, M. Dehghan and M. Razzaghi, Determination of a time-dependent parameter in a one-dimensional quasi-linear parabolic equation with temperature overspecification, Int. J. Comput. Math. 83 (2006) 905–913, https://doi.org/10.1080/00207160601117420.
[16] A. Saadatmandi and M. Dehghani, Computation of two time-dependent coefficients in a parabolic partial differential equation subject to additional specifications, Int. J. Comput. Math. 87 (2010) 997–1008, https://doi.org/10.1080/00207160802253958.
[17] M. Jamil and E. Y. K. Ng, Evaluation of meshless radial basis collocation method (RBCM) for heterogeneous conduction and simulation of temperature inside the biological tissues, Int. J. Therm. Sci. 68 (2013) 42–52, https://doi.org/10.1016/j.ijthermalsci.2013.01.007.
[18] S. A. Yousefi, Finding a control parameter in a one-dimensional parabolic inverse problem by using the Bernstein Galerkin method, Inverse Probl. Sci. Eng. 17 (2009) 821–828, https://doi.org/10.1080/17415970802583911.
[19] D. Lesnic, Identification of the time-dependent perfusion coefficient in the bio-heat conduction equation, J. Inverse Ill-Posed Probl. 17 (2009) 753–764, https://doi.org/10.1515/JIIP.2009.044.
[20] D. Lesnic and M. Ivanchov, Determination of the time-dependent perfusion coefficient in the bio-heat equation, Appl. Math. Lett. 39 (2015) 96–100, https://doi.org/10.1016/j.aml.2014.08.020.
[21] J. K. Grabski, D. Lesnic and B. T. Johansson, Identification of a time-dependent bioheat blood perfusion coefficient, Int. Commun. Heat Mass Transf. 75 (2016) 218–222, https://doi.org/10.1016/j.icheatmasstransfer.2015.12.028.
[22] A. Hazanee and D. Lesnic, Determination of a time-dependent coefficient in the bioheat equation, Int. J. Mech. Sci. 88 (2014) 259–266,
https://doi.org/10.1016/j.ijmecsci.2014.05.017.
[23] L. Cao, Q. H. Qin and N. Zhao, An RBFMFS model for analysing thermal behaviour of skin tissues, Int. J. Heat Mass Transf. 53 (2010) 1298–1307, https://doi.org/10.1016/j.ijheatmasstransfer.2009.12.036.
[24] K. Rashedi, Finding a time-dependent reaction coefficient of a nonlinear heat source in an inverse heat conduction problem, J. Math. Model. 12 (2024) 17–32,
https://doi.org/ 10.22124/JMM.2023.24413.2186.
[25] A. Saadatmandi and M. Dehghani, Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method, Numer. Methods Partial Differential Equations 26 (2010) 239–252, https://doi.org/10.1002/num.20442.
[26] M. Pourbabaae and A. Saadatmandi, The construction of a new operational matrix of the distributed-order fractional derivative using Chebyshev polynomials and its applications, Int. J. Comput. Math. 98 (2021) 2310–2329, https://doi.org/10.1080/00207160.2021.1895988.
[27] A. Saadatmandi and M. R. Azizi, Chebyshev finite difference method for a two-point boundary value problems with applications to chemical reactor theory, Iranian J. Math. Chem. 3 (2012) 1–7, https://doi.org/10.22052/IJMC.2012.5197.
[28] B. Salehi, L. Torkzadeh and K. Nouri, Chebyshev cardinal wavelets for nonlinear Volterra integral equations of the second kind, Math. Interdisc. Res. 7 (2022) 281–299, https://doi.org/10.22052/MIR.2022.243395.1325.
[29] P. C. Hansen, Analysis of discrete ill-posed problems by means of the L-curve, SIAM Rev. 34 (1992) 561–580, https://doi.org/10.1137/1034115.
[30] P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, 2010.
[31] K. Rashedi, A spectral method based on Bernstein orthonormal basis functions for solving an inverse Rosenau equation, Comp. Appl. Math. 41 (2022) p. 214, https://doi.org/10.1007/s40314-022-01908-0.
[32] T. Wei and M. Li, High order numerical derivatives for one-dimensional scattered noisy data, Appl. Math. Comput. 175 (2006) 1744–1759, https://doi.org/10.1016/j.amc.2005.09.018.
[33] J. Wen, M. Yamamoto and T. Wei, Simultaneous determination of a time-dependent heat source and the initial temperature in an inverse heat conduction problem, Inverse Probl. Sci. Eng. 21 (2013) 485–499, https://doi.org/10.1080/17415977.2012.701626.
[34] K. Rashedi, A numerical solution of an inverse diffusion problem based on operational matrices of orthonormal polynomials, Math. Methods Appl. Sci. 44 (2021) 12980–12997, https://doi.org/10.1002/mma.7601.
[35] K. Rashedi, Reconstruction of a time-dependent coefficient in nonlinear Klein–Gordon equation using Bernstein spectral method, Math. Methods Appl. Sci. 46 (2023) 1752–1771, https://doi.org/10.1002/mma.8607.
[36] M. Abbaszadeh, M. Dehghan and I. M. Navon, A POD reduced-order model based on spectral Galerkin method for solving the space-fractional Gray-Scott model with error estimate, Eng. Comput. 38 (2022) 2245–2268, https://doi.org/10.1007/s00366-020-01195-5.
)