Russian version English version
Volume 11   Issue 2   Year 2016
References

 

  1. Murphy S.V., Atala A. Organ engineering – combining stem cells, biomaterials, and bioreactors to produce bioengineered organs for transplantation. Bioessays. 2012;35:163-172. doi: 10.1002/bies.201200062
  2. Kirilova I.A., Sharkeev Yu.P., Nikolaev S.V., Podorozhnaya V.T., Uvarkin P.V., Ratushnyak A.S., Chebodaeva V.V. Physicomechanical properties of the extracellular matrix of a demineralized bone. AIP Conference Proceedings. 2016;1760:020027-1-020027-7. doi: 10.1063/1.4960246
  3. Penenko V.V. Metody chislennogo modelirovaniia atmosfernykh protsessov (Methods of numerical modeling of atmospheric processes). Leningrad; 1981. 352 p. (in Russ.).
  4. Alifanov O.M., Artiukhin E.A., Rumiantsev S.V. Ekstremal'nye metody resheniia nekorrektnykh zadach (Extreme methods for solving ill-posed problems). Moscow; 1988. 288 p. (in Russ.).
  5. Vasil'ev F.P. Chislennye metody resheniia ekstremal'nykh zadach (Numerical methods for solving extreme problems). Moscow; 1988. 550 p. (in Russ.).
  6. Kabanikhina S.I., Hasanovb A., Penenko A.V. The gradient-based method for solving the inverse coefficient heat-conduction problem. Numerical Analysis and Applications. 2008;1(1):34-45. doi: 10.1134/S1995423908010047
  7. Scherzer O., Grasmair M., Grossauer H., Haltmeier M., Lenzen F. Variational Methods in Imaging. Applied Mathematical Sciences. New York: Springer; 2009. 320 p.
  8. Godunov S.K., Antonov A.G., Kiriliuk O.P., Kostin V.I. Garantirovannaia tochnost' resheniia sistem lineinykh uravnenii v evklidovykh prostranstvakh (Guaranteed accuracy of solving systems of linear equations in Euclidean spaces). Novosibirsk; 1992. 360 p. (in Russ.).
  9. Cheverda V.A., Kostin V.I. R-pseudoinverse for compact operators in Hilbert space: existence and stability. J. Inverse and Ill-Posed Problems. 1995;3(2):131-148. doi: 10.1515/jiip.1995.3.2.131
  10. Gol'dman N.L. Inverse problems with final overdetermination for parabolic equations with unknown coefficients multiplying the highest derivative. Doklady Mathematics. 2011;83(3):316-320. doi: 10.1134/S1064562411030136
  11. Marchuk G.I. Formulations of some inverse problems. Dokl. Akad. Nauk SSSR. 1964;156(3):503-506 (in Russ.).
  12. Marchuk G.I. Chislennoe reshenie zadach dinamiki atmosfery i okeana (Numerical solutions for the dynamic problems of atmosphere and ocean). Leningrad; 1974 (in Russ.).
  13. Penenko V.V. In: Nekotorye problemy vychislitel'noi i prikladnoi matematiki (Some Problems of Computational and Applied Mathematics). Ed. Lavrent'ev M.M. Novosibirsk; 1975. P. 61-77 (in Russ.).
  14. Penenko A.V. In: Sibirskie elektronnye matematicheskie izvestiia. Trudy pervoi mezhdunarodnoi molodezhnoi shkoly-konferentsii "Teoriia i chislennye metody resheniia obratnykh i nekorrektnykh zadach" (Siberian Electronic Mathematical Reports: Proceedings of the First International Youth School-Conference "Theory and Computational Methods for Inverse and ill-posed problems”). Part I. Ed. Kabanikhin S.I. Novosibirsk; 2010. P. 178-198 (in Russ.).
  15. Penenko A.V. In: Sibirskie elektronnye matematicheskie izvestiia. Trudy vtoroi mezhdunarodnoi molodezhnoi shkoly-konferentsii ''Teoriia i chislennye metody resheniia obratnykh i nekorrektnykh zadach'' (Siberian Electronic Mathematical Reports: Proceedings of the First International Youth School-Conference "Theory and Computational Methods for Inverse and ill-posed problems”). Part II. Ed. Kabanikhin S.I. Novosibirsk; 2010. P. 320-339 (in Russ.).
  16. Hasanov A., DuChateau P., Pektas B. An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation. Journal of Inverse and Ill-Posed Problems. 2006;14(5):435-463. doi: 10.1515/156939406778247615
  17. Gokhberg I.Ts., Krein M.G. Vvedenie v teoriiu lineinykh nesamosopriazhennykh operatorov (Introduction to the theory of linear non-selfadjoint operators). Moscow; 1965. 448 p. (in Russ.).
  18. Kaltenbacher B. Some Newton-type methods for the regularization of nonlinear ill-posed problems. Inverse Problems. 1997;13(3):729-753. doi: 10.1088/0266-5611/13/3/012
  19. GNU Scientific Library Reference Manual Edition 2.2.1, for GSL Version 2.2.1. https://www.gnu.org/software/gsl/manual/html_node/ (accessed 25.10.2016).
Table of Contents Original Article
Alexey V. Penenko, Sergey V. Nikolaev, Sergey K. Golushko, Alexander V. Romashenko, Irina A. Kirilova Numerical Algorithms for Diffusion Coefficient Identification in Problems of Tissue Engineering. Ìàthematical biology and bioinformatics. 2016;11(2):426-444. doi: 10.17537/2016.11.426
(published in Russian)

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)
References

 

  Copyright IMPB RAS © 2005-2026