{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:29Z","timestamp":1760145749625,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T00:00:00Z","timestamp":1725235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union-NextGenerationEU","award":["BG-RRP-2.013-0001-C01"],"award-info":[{"award-number":["BG-RRP-2.013-0001-C01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We consider three integral observations inverse problems (IP1, IP2, IP3) for reconstruction of a time-dependent convection coefficient and a source in magnetohydrodynamics (MHD) model. On the first stage, using the integral observations, we reduce the inverse problems to nonclassical direct (forward) ones. The equivalence between the inverse and direct problems is established. Then, the well-posedness of nonclassical problems is proved. Further, to overcome the difficulties arising from the nonlinear nonlocal parabolic operators, we construct a linarization algorithm in time after their difference space discretizatons. Next, on each iteration, to solve the corresponding linear systems of algebraic equations, we propose adequate fast elimination algorithms. Computational results of test examples data are discussed.<\/jats:p>","DOI":"10.3390\/a17090387","type":"journal-article","created":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T10:07:35Z","timestamp":1725271655000},"page":"387","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Algorithms for Identification of Convection Coefficient and Source in a Magnetohydrodynamics Flow"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0866-3197","authenticated-orcid":false,"given":"Juri D.","family":"Kandilarov","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0684-8574","authenticated-orcid":false,"given":"Lubin G.","family":"Vulkov","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,2]]},"reference":[{"key":"ref_1","unstructured":"Alifanov, O.M., Artyukhin, E.A., and Rumyantsev, S.V. (2015). Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems, Begell House."},{"key":"ref_2","first-page":"517","article-title":"Diffusion subject to the specification of mass","volume":"115","author":"Canon","year":"1986","journal-title":"J. Math. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kabanikhin, S.I. (2011). Inverse and Ill-Posed Problems Theory and Applications, Walter de Gruyter.","DOI":"10.1515\/9783110224016"},{"key":"ref_4","first-page":"57","article-title":"Convergence of some iterative algorithms for numerical solution of two-dimentional non-stationary problems of magnetic hydrodynamics","volume":"35","author":"Krukovskiy","year":"2023","journal-title":"Math. Model."},{"key":"ref_5","unstructured":"Ladyzhenskaia, V.A., Solonnikov, V.A., and Ural\u2019tceva, N.N. (1986). Linear and Quasi-linear Equations of Parabolic Type, American Mathematical Society."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Samarskii, A.A., and Vabishchevich, P.N. (2007). Numerical Methods for Solving Inverse Problems of Mathematical Physics, Walter de Gruyter.","DOI":"10.1515\/9783110205794"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1134\/S1064562414020161","article-title":"Computational determination of the lowest order coefficient in a parabolic equation","volume":"89","author":"Vabishchevich","year":"2014","journal-title":"Dokl. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1080\/17415977.2014.993984","article-title":"Computational algorithms for solving the coefficient inverse problem for parabolic equations","volume":"24","author":"Vabishchevich","year":"2016","journal-title":"Inv. Probl. Sci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1080\/01630563.2017.1316996","article-title":"Investgation of a time-dependent source identification with integral overdetermination","volume":"38","author":"Ashyraliev","year":"2017","journal-title":"Numer. Funct. Anal. Optim."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Borzi, A. (2020). Modelling with Ordinary Differential Equations. A Comprehensive Approach, Chapman and Hall, CRC Press.","DOI":"10.1201\/9781351190398"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"101054","DOI":"10.1016\/j.jocs.2019.101054","article-title":"Computational recovery of time-dependent volatility from integral observations in option pricing","volume":"39","author":"Georgiev","year":"2019","journal-title":"J. Comput. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1016\/j.camwa.2016.01.017","article-title":"An integral constrained parabolic problem with applications in thermochronology","volume":"71","author":"Glotov","year":"2016","journal-title":"Comput. Math. Appl."},{"key":"ref_13","first-page":"552","article-title":"An inverse diffusion coefficient problem for a parabolic equation with integral constraint","volume":"15","author":"Glotov","year":"2018","journal-title":"Int. J. Numer. Anal. Model."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Evans, L.C. (2010). Partial Differential Equations, American Mathematical Society. [2nd ed.]. Graduate Studies in Mathematics 19.","DOI":"10.1090\/gsm\/019"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1093\/imanum\/dru015","article-title":"Unconditional convergence of the Euler semi-implicit scheme for the three dimensional incompressible MHD equations","volume":"33","author":"He","year":"2015","journal-title":"IMA J. Numer. Anal."},{"key":"ref_16","unstructured":"Isakov, V. (2006). Inverse Problems for Partial Differential Equations, Springer. [2nd ed.]."},{"key":"ref_17","unstructured":"Landau, L.D., Bell, J., Kearsley, M., Pitaevski, L., Lifshitz, E., and Sykes, J. (2013). Electrodynamics of Continuous Media, Elsevier. eBook ISBN 9781483293752."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s40306-024-00536-6","article-title":"Source identification for parabolic equations from integral observations by the finite difference splitting method","volume":"49","author":"Nguyen","year":"2024","journal-title":"Acta Math. Vietnam."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Samarskii, A.A., and Nikolaev, E.S. (1989). Numerical Methods for Grid Equations: Volume I Direct Methods, Birkh\u00e4user Verlag.","DOI":"10.1007\/978-3-0348-9272-8"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/j.cam.2016.08.015","article-title":"Identification of memory kernels in hyperbolic problems","volume":"311","author":"Slodicka","year":"2017","journal-title":"J. Comp. Appl. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1134\/S0965542509030087","article-title":"Optimal control asymptotics of a magnetohydrodynamic flow","volume":"49","author":"Tsyba","year":"2009","journal-title":"Comp. Math. Math. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Marchuk, G.I. (1995). Adjoint Equations and Analysis of Complex Systems, Kluwer Acad. Publishers.","DOI":"10.1007\/978-94-017-0621-6"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Koleva, M.N., and Vulkov, L.G. (2024). A Galerkin finite element method for reconstruction of time-dependent convection coefficients and source in a 1-D model of magnetohydrodynamics. Appl. Sci., 14.","DOI":"10.3390\/app14135949"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1579","DOI":"10.3934\/jimo.2018022","article-title":"Adjoint-based parameter and state estimation in 1-D magnetohydrodynamics (MHD) flow system","volume":"14","author":"Ren","year":"2018","journal-title":"J. Optim. Manag. Optim."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.apm.2016.08.021","article-title":"Comparison of the simplified and full MHD models for laminar incompressible flow past a circular cylinder","volume":"41","author":"Yu","year":"2017","journal-title":"Appl. Math. Model."},{"key":"ref_26","first-page":"178","article-title":"Solution of one problem for linear loaded parabolic type differential equation with integral conditions","volume":"7","author":"Khankishiyev","year":"2022","journal-title":"Adv. Math. Mod. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1134\/S0012266116070053","article-title":"Numerical identification of the leading coefficient of a parabolic equation","volume":"52","author":"Vabishchevich","year":"2016","journal-title":"Differ. Equ."},{"key":"ref_28","unstructured":"Kandilarov, J., and Vulkov, L. (2021, January 21\u201323). Simultaneous numerical reconstruction of time-dependent convection coefficient and source in magnetohydrodynamics flow system. Proceedings of the 16th Annual Meeting of the Bulgarian Section of SIAM, (BGSIAM\u201921) (to Appear), Sofia, Bulgaria."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/9\/387\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:47:29Z","timestamp":1760111249000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/9\/387"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,2]]},"references-count":28,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["a17090387"],"URL":"https:\/\/doi.org\/10.3390\/a17090387","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2024,9,2]]}}}