[1] H. Azari, Numerical procedures for the determination of the leading coefficient a(x), Proc. Appl. Math. Mech. 7 (2007) 2040003 - 2040004, https://doi.org/10.1002/pamm.200700080.
[2] H. Azari and S. Zhang, A numerical approximation to the solution of an inverse heat conduction problem, Numer. Methods Partial Differential Equations 26 (2010) 95 - 106, https://doi.org/10.1002/num.20418.
[3] C. W. Chang, C. H. Liu and C. C. Wang, Review of computational schemes in inverse heat conduction problems, Smart Sci. 6 (2018) 94 - 103,
https://doi.org/10.1080/23080477.2017.1408987.
[4] A. G. Fatullayev and S. Cula, An iterative procedure for determining an unknown spacewise-dependent coefficient in a parabolic equation, Appl. Math. Lett. 22 (2009) 1033 - 1037, https://doi.org/10.1016/j.aml.2009.01.022.
[5] M. S. Hussein, D. Lesnic and M. I. Ismailov, An inverse problem of finding the time-dependent diffusion coefficient from an integral condition, Math. Methods Appl. Sci. 39 (2016) 963 - 980, https://doi.org/10.1002/mma.3482.
[6] K. Rashedi, Recovery of coefficients of a heat equation by Ritz collocation method, Kuwait J. Sci. 50 (2023) 1-12, https://doi.org/10.48129/kjs.18581.
[7] A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Springer, New York, 2011.
[8] K. Rashedi, Reconstruction of a time-dependent wave source and the initial condition in a hyperbolic equation, Kuwait J. Sci. 51 (2024) #100104, https://doi.org/10.1016/j.kjs.2023.07.010.
[9] V. Isakov, On inverse problems in secondary oil recovery, European J. Appl. Math. 19 (2008) 459 - 478, https://doi.org/10.1017/S0956792508007365.
[10] A. A. Samarskii and P. N. Vabishchevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics, Berlin, Walter de Gruyter, 2007.
[11] J. R. Cannon and W. Rundell, Recovering a time dependent coefficient in a parabolic differential equation, J. Math. Anal. Appl. 160 (1991) 572 - 582, https://doi.org/10.1016/0022-247X(91)90327-V.
[12] M. I. Ivanchov, Inverse problems for the heat conduction with nonlocal boundary conditions, Ukrainian Math. J. 45 (1993) 1186 - 1192, https://doi.org/10.1007/BF01070965.
[13] M. I. Ivanchov and N. V. Pabyrivs’ka, Simultaneous determination of two coefficients of parabolic equation in the case of nonlocal and integral conditions, Ukrainian Math. J. 53 (2001) 674 - 684, https://doi.org/10.1023/A:1012570031242.
[14] F. Kanca and M. I. Ismailov, The inverse problem of finding the time-dependent diffusion coefficient of the heat equation from integral overdetermination data, Inverse Probl. Sci. Eng. 20 (2012) 463 - 476, https://doi.org/10.1080/17415977.2011.629093.
[15] H. M. Yin, Solvability of a class of parabolic inverse problems, Adv. Differential Equations 1 (1996) 1005 - 1023,
https://doi.org/10.57262/ade/1366895242.
[16] H. Azari, W. Allegretto, Y. Lin and S. Zhang, Numerical procedures for recovering a time dependent coefficient in a parabolic differential equation, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 11 (2004) 181-199.
[17] D. Lesnic, S. A. Yousefi and M. Ivanchov, Determination of a time-dependent diffusivity from nonlocal conditions, J. Appl. Math. Comput. 41 (2013) 301-320, https://doi.org/10.1007/s12190-012-0606-4.
[18] S. A. Yousefi, D. Lesnic and Z. Barikbin, Satisfier function in Ritz–Galerkin method for the identification of a time-dependent diffusivity, J. Inverse Ill-Posed Probl. 20 (2012) 701 - 722, doi.org/10.1515/jip-2012-0020.
[19] M. Shamsi and M. Dehghan, Recovering a time-dependent coefficient in a parabolic equation from overspecified boundary data using the pseudospectral Legendre method, Numer. Methods Partial Differential Equations 23 (2007) 196 - 210, https://doi.org/10.1002/num.20174.
[20] M. Lakestani and M. Dehghan, The use of Chebyshev cardinal functions for the solution of a partial differential equation with an unknown time-dependent coefficient subject to an extra measurement, J. Comput. Appl. Math. 235
(2010) 669 - 678, https://doi.org/10.1016/j.cam.2010.06.020.
[21] J. R. Cannon and H. M. Yin, Numerical solutions of some parabolic inverse problems, Numer. Methods Partial Differential Equations 6 (1990) 177-191, https://doi.org/10.1002/num.1690060207.
[22] M. Dehghan and M. Tatari, Solution of a parabolic equation with time-dependent coeeficient and an extra measurement using the decomposition procedure of Adomian, Phys. Scr. 72 (2005) #425, https://doi.org/10.1088/0031-8949/72/6/001.
[23] B. Hu and H. M. Yin, Determination of the leading coefficient a(x) in the heat equation u_{t} = a(x)\Delta u, Quart. Appl. Math. 51 (1993) 577 - 583, https://doi.org/10.1090/qam/1233531.
[24] A. Erdem, A numerical method based on the polynomial regression for the inverse diffusion problem, Int. J. Comput. Math. 92 (2015) 1883 - 1894, https://doi.org/10.1080/00207160.2014.884712.
[25] P. N. Vabishchevich, Computational identification of the lowest space-wise dependent coefficient of a parabolic equation, Appl. Math. Model. 65 (2019) 361 - 376, https://doi.org/10.1016/j.apm.2018.08.024.
[26] A. Hasanov, B. Pektas and A. Erdem, Comparative analysis of inverse coefficient problems for parabolic equations, Part I: adjoint problem approach, Inverse Probl. Sci. Eng. 19 (2011) 599 - 615,
https://doi.org/10.1080/17415977.2011.579605.
[27] A. Hasanov and B. Pektas, Comparative analysis of inverse coefficient problems for parabolic equations. Part III: conjugate gradient method and coarse-fine grid algorithm, Inverse Probl. Sci. Eng. 19 (2011) 633 - 657, https://doi.org/10.1080/17415977.2011.579607.
[28] B. Pektas, Determination of unknown coefficients in a nonlocal parabolic problem from Neumann type boundary measured data, Adv. Dyn. Syst. Appl. 5 (2010) 215 - 230.
[29] 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.
[30] W. W. Bell, Special Functions for Scientists and Engineers, Dover Publications, New York, 2004.
[31] H. Hochstadt, The Functions of Mathematical Physics, Dover Publications, New York, 1986.
[32] A. Saadatmandi and M. Dehghan, A Legendre collocation method for fractional integro-differential equations, J. Vib. Control 17 (2011) 2050 - 2058, https://doi.org/10.1177/1077546310395977.
[33] M. Sabzevari and F. Molaei, Numerical solution of system of nonlinear integro-differential equations using hybrid of Legendre polynomials and block-pulse functions, Math. Interdisc. Res. 5 (2020) 225 - 238, https://doi.org/10.22052/MIR.2019.173293.1119.
[34] A. Saadatmandi and M. Mohabbati, Numerical solution of fractional telegraph equation via the tau method, Math. Rep. (Bucur.) 17 (2015) 155-166.
[35] A. Sarraf, F. Baharifard and K. Rashedi, A decoupled physics-informed neural network for recovering a space-dependent force function in the wave equation from integral overdetermination data, Comput. Appl. Math. 42 (2023) #178, https://doi.org/10.1007/s40314-023-02323-9.
[36] D. A. Murio, The Mollification Method and the Numerical Solution of Ill-Posed Problems, New York, Wiley Interscience, 1993.
[37] 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.
[38] K. Rashedi, Retrieving the transient temperature field and blood perfusion coefficient in the Pennes bioheat equation subject to nonlocal and convective boundary conditions, Iranian J. Math. Chem. 15 (2024) 91 - 105,
https://doi.org/10.22052/IJMC.2024.254475.1837.
[39] 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.
)