Open Access
Issue
BIO Web Conf.
Volume 97, 2024
Fifth International Scientific Conference of Alkafeel University (ISCKU 2024)
Article Number 00039
Number of page(s) 10
DOI https://doi.org/10.1051/bioconf/20249700039
Published online 05 April 2024
  • A. G. Goncharskii, A.V. Leonov, A.S. Yagola, “Finite-Difference Approximation of Linear Ill-Posed Problems,” Zh. Vych. Mat. Mat. Fiz, vol. 14, no. 4, pp. 1022–1027, 1974. [Google Scholar]
  • V. K. Ivanov, V. V. Vasin, and T.V.P., Theory of Linear Ill-Posed Problem and Application. Nauok Moscow, 1978. [Google Scholar]
  • V. P. Tanana, “Projection methods and finite-difference approximation of linear incorrectly formulated problems,” Sib. Math. J., vol. 16, no. 6, pp. 999–1004, 1975, DOI: 10.1007/BF00967398. [Google Scholar]
  • V. V. Vasin, “Discrete convergence and finite-dimensional approximation of regularizing algorithms,” USSR Comput. Math. Math. Phys., vol. 19, no. 1, pp. 8–19, 1979, DOI: 10.1016/0041-5553(79)90062-4. [CrossRef] [Google Scholar]
  • S. A. Noaman, H. K. Al-Mahdawi, B. T. Al-Nuaimi, and A. I. Sidikova, “Iterative method for solving linear operator equation of the first kind,” MethodsX, vol. 10, p. 102210, 2023. [CrossRef] [PubMed] [Google Scholar]
  • B. T. Al-Nuaimi, H. K. Al-Mahdawi, Z. Albadran, H. Alkattan, M. Abotaleb, and E.-S. M. Elkenawy, “Solving of the Inverse Boundary Value Problem for the Heat Conduction Equation in Two Intervals of Time,” Algorithms, vol. 16, no. 1, p. 33, 2023. [CrossRef] [Google Scholar]
  • V. P. Tanana and A. I. Sidikova, “On Estimating the Error of an Approximate Solution Caused by the Discretization of an Integral Equation of the First Kind,” Proc. Steklov Inst. Math., vol. 299, no. 1, pp. 217–224, 2017, DOI: 10.1134/S0081543817090231. [CrossRef] [Google Scholar]
  • V. P. Tanana, E. Y. Vishnyakov, and A. I. Sidikova, “An approximate solution of a Fredholm integral equation of the first kind by the residual method,” Numer. Anal. Appl., vol. 9, no. 1, pp. 74–81, 2016, DOI: 10.1134/S1995423916010080. [Google Scholar]
  • H. K. Al-Mahdawi, A. I. Sidikova, H. Alkattan, M. Abotaleb, A. Kadi, and E.-S. M. Elkenawy, “Parallel Multigrid Method for Solving Inverse Problems,” MethodsX, p. 101887, 2022. [CrossRef] [PubMed] [Google Scholar]
  • A. I. Sidikova and H. K. Al-Mahdawi, “The solution of inverse boundary problem for the heat exchange for the hollow cylinder,” in AIP Conference Proceedings, 2022, vol. 2398, no. 1, p. 60050. [Google Scholar]
  • H. K. Al-Mahdawi and A. I. Sidikova, “Iterated Lavrent’ev regularization with the finitedimensional approximation for inverse problem,” in AIP Conference Proceedings, 2022, vol. 2398, no. 1, p. 60080. [Google Scholar]
  • H. K. I. Al-Mahdawi, M. Abotaleb, H. Alkattan, A.-M. Z. Tareq, A. Badr, and A. Kadi, “Multigrid Method for Solving Inverse Problems for Heat Equation,” Mathematics, vol. 10, no. 15, p. 2802, 2022. [CrossRef] [Google Scholar]
  • H. K. I. Al-Mahdawi, H. Alkattan, M. Abotaleb, A. Kadi, and E.-S. M. El-Kenawy, “Updating the Landweber Iteration Method for Solving Inverse Problems,” Mathematics, vol. 10, no. 15, p. 2798, 2022. [CrossRef] [Google Scholar]
  • H. K. Al-Mahdawi, Z. Albadran, H. Alkattan, M. Abotaleb, K. Alakkari, and A. J. Ramadhan, “Using the inverse Cauchy problem of the Laplace equation for wave propagation to implement a numerical regularization homotopy method,” in AIP Conference Proceedings, 2023, vol. 2977, no. 1. [Google Scholar]
  • R. Plato, P. Mathé, and B. Hofmann, “Optimal rates for Lavrentiev regularization with adjoint source conditions,” Math. Comput., vol. 87, no. 310, pp. 785–801, 2018. [Google Scholar]
  • R. Plato, “The Product Midpoint Rule for Abel-Type Integral Equations of the First Kind with Perturbed Data,” in New Trends in Parameter Identification for Mathematical Models, Springer, 2018, pp. 195–225. [CrossRef] [Google Scholar]
  • V. B. Glasko, N. I. Kulik, I. N. Shklyarov, and A. N. Tikhonov, “An inverse problem of heat conductivity,” Zhurnal Vychislitel’noi Mat. i Mat. Fiz., vol. 19, no. 3, pp. 768–774, 1979. [Google Scholar]
  • A. S. Belonosov and M. A. Shishlenin, “Continuation problem for the parabolic equation with the data on the part of the boundary,” Siber. Electron. Math. Rep., vol. 11, pp. 2234, 2014. [Google Scholar]
  • S. I. Kabanikhin, A. Hasanov, and A. V. Penenko, “A gradient descent method for solving an inverse coefficient heat conduction problem,” Numer. Anal. Appl., vol. 1, no. 1, pp. 34–45, 2008. [Google Scholar]
  • A. G. Yagola, I. E. Stepanova, Y. Van, and V. N. Titarenko, “Obratnye zadachi i metody ikh resheniya. Prilozheniya k geofizike,” Inverse Probl. Methods their Solut. Appl. to Geophys. Moscow Binom. Lab. znanii, 2014. [Google Scholar]
  • S. I. Kabanikhin, O. I. Krivorot’ko, and M. A. Shishlenin, “A numerical method for solving an inverse thermoacoustic problem,” Numer. Anal. Appl., vol. 6, no. 1, pp. 3439, 2013. [Google Scholar]
  • V. P. Tanana, “On the order-optimality of the projection regularization method in solving inverse problems,” Sib. Zhurnal Ind. Mat., vol. 7, no. 2, pp. 117–132, 2004. [Google Scholar]
  • M. Hajihassani, D. Jahed Armaghani, and R. Kalatehjari, “Applications of particle swarm optimization in geotechnical engineering: a comprehensive review,” Geotech. Geol. Eng., vol. 36, pp. 705–722, 2018. [CrossRef] [Google Scholar]
  • O. U. Rehman, S. U. Rehman, S. Tu, S. Khan, M. Waqas, and S. Yang, “A quantum particle swarm optimization method with fitness selection methodology for electromagnetic inverse problems,” IEEE Access, vol. 6, pp. 63155–63163, 2018. [CrossRef] [Google Scholar]
  • G. V. Alekseev and D. A. Tereshko, “Particle swarm optimization-based algorithms for solving inverse problems of designing thermal cloaking and shielding devices,” Int. J. Heat Mass Transf., vol. 135, pp. 1269–1277, 2019. [CrossRef] [Google Scholar]
  • J. L. G. Pallero et al., “Particle swarm optimization and uncertainty assessment in inverse problems,” Entropy, vol. 20, no. 2, p. 96, 2018. [CrossRef] [PubMed] [Google Scholar]
  • B. Zhang, H. Qi, S.-C. Sun, L.-M. Ruan, and H.-P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Transf., vol. 85, pp. 300–310, 2015. [CrossRef] [Google Scholar]
  • R. Perera, S.-E. Fang, and A. Ruiz, “Application of particle swarm optimization and genetic algorithms to multiobjective damage identification inverse problems with modelling errors,” Meccanica, vol. 45, pp. 723–734, 2010. [CrossRef] [Google Scholar]
  • Tanana V.P., “on an iterative projectin algorithm for first-order operator equations with perturbed operator,” Dokl. AN SSSR, vol. 224, no. 15, pp. 1025–1029, 1975. [Google Scholar]
  • V. P. Tanana, “On an iterative projection algorithm for solving ill posed problems with an approximately specified operator,” USSR Comput. Math. Math. Phys., vol. 17, no. 1, pp. 12–20, 1977, DOI: 10.1016/0041-5553(77)90065-9. [CrossRef] [Google Scholar]
  • A. N. Tikhonov, “On the solution of ill-posed problems and the method of regularization,” Dokl. Akad. Nauk SSSR, vol. 151, no. 3, pp. 501–504, 1963. [Google Scholar]
  • A. V. Goncharskii, A. S. Leonov, and A. G. Yagola, “A generalized discrepancy principle,” USSR Comput. Math. Math. Phys., vol. 13, no. 2, pp. 25–37, 1973, DOI: 10.1016/0041-5553(73)90128-6. [CrossRef] [Google Scholar]
  • R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in MHS’95. Proceedings of the sixth international symposium on micro machine and human science, 1995, pp. 39–43. [Google Scholar]
  • P. C. Hansen, “Regularization tools version 4.0 for Matlab 7.3,” Numer. algorithms, vol. 46, pp. 189–194, 2007. [Google Scholar]

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