1
University of Diyala, Diyala ,32001, Iraq
(hssnkd@gmail.com)
2
University of Diyala, Diyala ,32001, Iraq
(alkattan.hussein92@gmail.com)
3
Department of System Programming, South Ural State University, Chelyabinsk 454080, Russia
(alhumaimaali@uodiyala.edu.iq)
4
Electronics and Communications Engineering Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa City 11152, Egypt
(skenawy@ieee.org)
5
Faculty of Artificial Intelligence, Delta University for Science and Technology, Mansoura, Egypt
(mmm@ieee.org)
6
University of Diyala, Diyala ,32001, Iraq
(anfal6011@gmail.com)
7
Faculty of Artificial Intelligence, Delta University for Science and Technology, Mansoura, Egypt
(jinanabdullahmahmood@gmail.com)
Abstract :
In this paper, we display the definition and arrangement of the beginning esteem issue in composite materials for warm condition. The issue includes finding the starting temperature conveyance when as it were the temperature spreading at time t=T>0 is given. Typically, a challenging issue since it has a place to a course of numerically unsteady issues that are ill-posed. To characterize this issue, we have to be present work spaces and unravel the coordinate issue to decide them. The method of division of factors is commonly utilized to fathom the coordinate issue, but it isn't reasonable for the due to the expansive blunders and disparate arrangement it produces. Ivanov V.K. proposed a strategy to get a steady inexact arrangement by supplanting the coming about arrangement with a fractional whole that depends on δ, N=N(δ). Another approach is the Picard strategy that employments a family of administrators to map the space into itself and get a regularized inexact arrangement. We show the comes about of computational tests and assess the viability of the Picard strategy.
Keywords :
inverse problem; Picard method; ill-posed problem; composite material;
References :
[1] S I Kabanikhin, Inverse and ill-posed problems: theory and applications, 55. Walter De Gruyter, 2011.
[2] S I Kabanikhin, Inverse and ill-posed problems. de Gruyter, 2011.
[3] S I Kabanikhin, INVERSE AND ILL-POSED PROBLEMS. Sib. Elektron. Mat. Izv., 7, 2010.
[4] A G Goncharskii, AV Leonov, A S, Yagola, Finite-Difference Approximation of Linear Ill-Posed Problems. Zh. Vych. Mat. Mat. Fiz, 14(4), 1022–1027, 1974.
[5] V K. Ivanov, V V Vasin, T V P, Theory of Linear Ill-Posed Problem and Application. Nauok Moscow, 1978.
[6] V P Tanana, Projection methods and finite-difference approximation of linear incorrectly formulated problems. Sib. Math. J., 16(6), 999–1004, 1975.
[7] V V Vasin, Discrete convergence and finite-dimensional approximation of regularizing algorithms. USSR Comput. Math. Math. Phys., 19(1), 8–19, 1979.
[8] 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., 299(1), 217–224, 2017.
[9] V P Tanana, E Y Vishnyakov, A I Sidikova, An approximate solution of a Fredholm integral equation of the first kind by the residual method. Numer. Anal. Appl., 9(1), 74–81, 2016.
[10] B T Al-Nuaimi, H K Al-Mahdawi, Z Albadran, H Alkattan, M Abotaleb, E-S M El-kenawy, Solving of the Inverse Boundary Value Problem for the Heat Conduction Equation in Two Intervals of Time. Algorithms, 16(1), 33, 2023.
[11] G G Skorik,V V Vasin, Regularized Newton type method for retrieval of heavy water in atmosphere by IR spectra of the solar light transmission. Eurasian J. Math. Comput. Appl., 7(2), 79–88, 2019.
[12] L D Menikhes, V P Tanana, The finite-dimensional approximation for the Lavrent’ev method. Sib. Zhurnal Vychislitel’noi Mat., 1(1), 59–66, 1998.
[13] A I Sidikova, H K Al-Mahdawi, The solution of inverse boundary problem for the heat exchange for the hollow cylinder. in AIP Conference Proceedings, 2398(1) 2022.
[14] H K I Al-Mahdawi, M Abotaleb, H Alkattan, A M Z Tareq, A Badr, A Kadi, Multigrid Method for Solving Inverse Problems for Heat Equation. Mathematics, 10(15), 2802, 2022.
[15] H K I Al-Mahdawi, H Alkattan, M Abotaleb, A Kadi, E-S M El-kenawy, Updating the Landweber Iteration Method for Solving Inverse Problems,” Mathematics, 10(15), 2798, 2022.
[16] H K Al-Mahdawi, A I Sidikova, H Alkattan, M Abotaleb, A Kadi, E-S M El-kenawy, Parallel Multigrid Method for Solving Inverse Problems. MethodsX, 101887, 2022.
[17] S A Noaman, H K Al-Mahdawi, B T Al-Nuaimi, A I Sidikova, Iterative method for solving linear operator equation of the first kind,” MethodsX, 10, 102210, 2023.
[18] R Plato, P Mathé, B Hofmann, Optimal rates for Lavrentiev regularization with adjoint source conditions. Math. Comput., 87(310), 785–801, 2018.
[19] 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, 195–225,2018.
[20] V B Glasko, N I Kulik, I N Shklyarov, A N Tikhonov, An inverse problem of heat conductivity. Zhurnal Vychislitel’noi Mat. i Mat. Fiz., 19(3), 768–774, 1979.
[21] A S Belonosov, M A Shishlenin, Continuation problem for the parabolic equation with the data on the part of the boundary. Siber. Electron. Math. Rep., 11, 22–34, 2014.
[22] S I Kabanikhin, A Hasanov, A V Penenko, A gradient descent method for solving an inverse coefficient heat conduction problem, Numer. Anal. Appl., 1(1), 34–45, 2008.
[23] A G Yagola, I E Stepanova, Y Van, 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.
[24] S I Kabanikhin, O I Krivorot’ko, M A Shishlenin, A numerical method for solving an inverse thermoacoustic problem,” Numer. Anal. Appl., 6(1), 34–39, 2013.
[25] V P Tanana, On the order-optimality of the projection regularization method in solving inverse problems. Sib. Zhurnal Ind. Mat., 7(2), 117–132, 2004.
[26] A N Tikhonov, A A Samarskii, Equations of mathematical physics. Courier Corporation, 2013.
[27] H K Al-Mahdawi, M Abotaleb, H Alkattan, E-S M El-Kenawy, E M Mohamed, Solving the Inverse Initial Value Problem for the Heat Conductivity Equation by Using the Picard Method.
[28] V P Tanana, A A Ershova, On the solution of an inverse boundary value problem for composite materials. Vestn. Udmurt. Univ. Mat. Mekhanika. Komp’yuternye Nauk., 28(4), 474–488, 2018.
| Style | # |
|---|---|
| MLA | Al-Mahdawi H. K., Alhumaima Ali Subhi, Hussein Alkattan, Mohamed Saber , Marwa M. Eid , Anfal A. Sabti Al-Mahdawi, Jinan A. M. Al-Saddaee. "Solving Initial Value Problem in Composite Materials for Heat Equation." Journal of Artificial Intelligence and Metaheuristics, Vol. 6, No. 1, 2023 ,PP. 08-17 (Doi : https://doi.org/10.54216/JAIM.060101) |
| APA | Al-Mahdawi H. K., Alhumaima Ali Subhi, Hussein Alkattan, Mohamed Saber , Marwa M. Eid , Anfal A. Sabti Al-Mahdawi, Jinan A. M. Al-Saddaee. (2023). Solving Initial Value Problem in Composite Materials for Heat Equation. Journal of Journal of Artificial Intelligence and Metaheuristics, 6 ( 1 ), 08-17 (Doi : https://doi.org/10.54216/JAIM.060101) |
| Chicago | Al-Mahdawi H. K., Alhumaima Ali Subhi, Hussein Alkattan, Mohamed Saber , Marwa M. Eid , Anfal A. Sabti Al-Mahdawi, Jinan A. M. Al-Saddaee. "Solving Initial Value Problem in Composite Materials for Heat Equation." Journal of Journal of Artificial Intelligence and Metaheuristics, 6 no. 1 (2023): 08-17 (Doi : https://doi.org/10.54216/JAIM.060101) |
| Harvard | Al-Mahdawi H. K., Alhumaima Ali Subhi, Hussein Alkattan, Mohamed Saber , Marwa M. Eid , Anfal A. Sabti Al-Mahdawi, Jinan A. M. Al-Saddaee. (2023). Solving Initial Value Problem in Composite Materials for Heat Equation. Journal of Journal of Artificial Intelligence and Metaheuristics, 6 ( 1 ), 08-17 (Doi : https://doi.org/10.54216/JAIM.060101) |
| Vancouver | Al-Mahdawi H. K., Alhumaima Ali Subhi, Hussein Alkattan, Mohamed Saber , Marwa M. Eid , Anfal A. Sabti Al-Mahdawi, Jinan A. M. Al-Saddaee. Solving Initial Value Problem in Composite Materials for Heat Equation. Journal of Journal of Artificial Intelligence and Metaheuristics, (2023); 6 ( 1 ): 08-17 (Doi : https://doi.org/10.54216/JAIM.060101) |
| IEEE | Al-Mahdawi H. K., Alhumaima Ali Subhi, Hussein Alkattan, Mohamed Saber, Marwa M. Eid, Anfal A. Sabti Al-Mahdawi, Jinan A. M. Al-Saddaee, Solving Initial Value Problem in Composite Materials for Heat Equation, Journal of Journal of Artificial Intelligence and Metaheuristics, Vol. 6 , No. 1 , (2023) : 08-17 (Doi : https://doi.org/10.54216/JAIM.060101) |