Чисельне розв’язування iнтегральних рiвнянь. Чисельне розв’язування лінійних і нелінійних обернених задач.

• Лінійні інтегральні рівняння (прикладна математика, бакалаври)
• Методи регуляризації для розв'язування обернених задач (прикладна математика, 1.9)
• Методи регуляризації для розв'язування обернених задач (прикладна математика,магістри)
• Чисельні методи (комп'ютерні науки)
• Чисельні методи (прикладна математика,бакалаври)
• Науковий семінар (прикладна математика,магістри)

1. Chapko R., Kress R., Yoon J.-R. On the numerical solution of an inverse boundary value problem for the heat equation // Inverse Problems.- 1998.- 14.- No 4.- P. 853-867.
2. Chapko R. On the numerical solution of direct and inverse problems for the heat equation in a semi-infinite region // Journal of Computational and Applied Mathematics.- 1999.- 108.- No 1-2.- P. 41-55.
3. Chapko R., Kress R., Yoon J.-R. An inverse boundary value problem for the heat equation: the Neumann condition // Inverse Problems.- 1999.- 15.- No 4.- P. 1033-1046.
4. Gavrilyuk I., Makarov V., Chapko R. On the numerical solution of linear evolution problems with an integral operator coefficient // Journal of Integral Equations and Applications.- 1999.- 11.- No1.- P. 37-56.
5. Chapko R., Kress R. On the numerical solution of initial boundary value problems by the Laguerre transformation and boundary integral equations // In: Integral and Integrodifferential Equations: Theory, Methods and Applications. Series in Mathematical Analysis and Applications. Vol. 2 (Agarwal, O’Regan eds.). Gordon and Breach Science Publishers. Amsterdam.- 2000.- P. 55-69.
6. Chapko R., Kress R., Mönch L. On the numerical solution of a hypersingular integral equation for elastic scattering from a planar crack // IMA Journal for Numerical Analysis.- Vol. 20.- 2000.- P. 601-619.
7. Chapko R. On the combination of Rothe’s method and boundary integral equations for the nonstationary Stokes equation // Journal of Integral Equations and Applications.- Vol. 13.- 2001.- P. 99-116.
8. Chapko R. On the numerical solution of the first initial boundary value problems for heat equation in the torus case // Journal of Engineering Mathematics.- 2002.- 43.- P. 75-87.
9. Chapko R. The numerical solution of the evolution problem of the second order in time on the closed smooth boundary // Journal of Computational and Applied Mathematics.- 2002.- 145.- P. 493-503.
10. Chapko R. On the numerical solution of a boundary value problem in the plane elasticity for a double-connected domain // Mathematics and Computers in Simulation.- 2004.- 66.- P. 425-438.
11. Chapko R. An integral equation method for the numerical analysis of gravity waves in a channel with free boundary // Applied Mathematics and Computation.- 2004.- 159.- P. 247-266.
12. Chapko R., Kügler Ph. A comparison of the Landweber method and the Gauss-Newton method for an inverse parabolic boundary value problem // Journal of Computational and Applied Mathematics.- 2004.-169.- P. 183-196.
13. Chapko R., Kress R. A hybrid method for inverse boundary value problems in potential theory // Journal of Ill-Posed and Inverse Problems.- 2005.- 13.- P. 1-14.
14. Chapko R., Vintonyak N. A hybrid method for inverse boundary value problems for an inclusion in semi-infinite two-dimensional domains // Journal of Integral Equations and Applications.- Vol. 19.- 2007.- P. 311-333.
15. Chapko R., Datsiv G. The numerical solution of the axially symmetric linear sloshing problem by the boundary integral equation method // Journal of Integral Equations and Applications.- 20.- 2008.- P. 409-436.
16. Chapko R., Johansson B.T. An alternanting boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions // Inverce Problems and Imaging.- 2.- 2008.- P. 317-333.
17. Chapko R., Johansson B.T. An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut // Computational Methods in Applied Mathematics.- 2008.- 8.- P. 315-335.
18. Chapko R. On a hybrid method for shape reconstruction of buried object in an elastostatic half plane // Inverce Problems and Imaging.- 2009.- 3.- P. 199-210.
19. Chapko R., Johansson B.T. On some iterative methods based on boundary integrals for elliptic Cauchy problems in semi-infinite domains // Electronic Journal of Boundary Elements.- 2009.- 7.- P. 1-12.
20. Chapko R., Johansson B.T. An alternating boundary integral based method for a Cauchy problem for the Laplace equation in a quadrant // Inverse Problems in Science and Engineering.- 2009.- 17.- P. 871-883.
21. Chapko R., Vintonyak N. On the convergence analysis of the hybrid method for an inverse boundary value potential problem // Matematychni studii.- 2009.- 23.- С.56-63.
22. Chapko R., Johansson B.T. An alternating boundary integral based method for inverse potential flow around immersed bodies // Journal of Numerical and Applied Mathematics.- 2009.- 97.- P. 10-25.
23. Chapko R., Vavrychuk V. On the numerical solution of a mixed initial boundary value problem for the heat equation in a double-connected planar domain // Journal of Numerical and Applied Mathematics.- 2009.- 97.- P. 26-38.
24. Chapko R., Johansson B.T., Sobeyko O. On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion  // CMES: Computer Modelling in Engineering & Sciences.- 2010.- 62.-P.57-75.
25. Chapko R., Johansson B.T., Vavrychuk V. Recovering boundary data in planar heat conduction using a boundary integral equation method // Electronic Journal of Boundary Elements.- 2011.- 9.-P.1-15.
26. Chapko R., Johansson B.T. On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach // Inverse Problems and Imaging, 2012.- 6. – P. 25-38.
27. Chapko R., Johansson B.T., Protsyuk O. A direct boundary integral equation method for the numerical construction of harmonic functions in three-dimensional layered domains containing a cavity // International Journal of Computer Mathematics, 2012.- 89.- P.1448-1462.
28. Chapko R., Johansson B.T. A direct integral equation method for a Cauchy problem for the Laplace equation in 3-dimensional semi-infinite domains // CMES: Computer Modelling in Engineering & Sciences, 2012.- 85.- No. 2.- P. 105-128.
29. Chapko R., Ivanyshyn O., Protsyuk O. On a nonlinear integral equation approach for the surface reconstruction in semi-infinite layered domains // Inverse Problems in Science and Engineering, 2013.- 27.- P. 547-561.
30. Chapko R., Johansson B.T., Vavrychuk V. A projected iterative method based on integral equations for inverse heat conduction in domains with a cut // Inverse Problems. – 2013. –29. -DOI:10.1088/0266-5611/29/6/065003. – P.1-17.
31. Chapko R., Johansson B.T., Savka Y.  On the use of an integral equation approach for the numerical solution of a Cauchy problem for Laplace equation in a doubly connected planar domain //  Inverse Problems in Science and Engineering, 2013.- 22.- P.130-149.
32. Chapko R., Johansson B.T., Vavrychuk V. Numerical solution of parabolic Cauchy problems in planar corner domains // Mathematics and Computers in Simulation, 2014.- 101.- P. 1-12.
33. Babenko C., Chapko R., Khlobystov V., Makarov V. On the interpolation of a function on a bounded domain by its traces on parametric hypersurfaces // International Journal of Computer Mathematics, 2014.- 91.- P.1673-1682.
34. Babenko C., Chapko R., Johansson B.T. On the use of integral equation approach for the numerical solution of a Cauchy problem for Laplace equation in a doubly connected planar domain // CMES: Computer Modeling in Engineering & Sciences, 2014.- 101.- P. 299-317.
35. Borachok I., Chapko R., Johansson B.T. Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations // Journal of Inverse and Ill-Posed Problems, 2016.- 24.-P. 711–725.
36. Borachok I., Chapko R., Johansson B.T. Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations // Inverse Problems in Science and Engineering, 2016.- 24.- P. 1550 -1568.
37. Chapko R., Johansson B.T. Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations // Journal of Engineering Mathematics, 2017.- 103.- P.23-37.
38. Chapko R.S., Ivanyshyn Yaman O.M., Kanafotskyi T.S. On the non-linear integral equation approaches for the boundary reconstruction in double-connected planar domains // Journal of Numerical and Applied Mathematics , 2016.-  122.- P.7-20.
39. Chapko R., Johansson B.T. A boundary integral approach for numerical solution of the Cauchy problem for the Laplace equation // Ukrainian Mathematical Journal, 2016.- 68.- P.1665-1682.
40. Chapko R.S., Johansson B.T., Shkolyk M.V. On a boundary integral equation method for elastostatic Cauchy problems in annular planar domains // Journal of Numerical and Applied Mathematics, 2017.- 126.- P.16–32.
41. Chapko R., Gintides D., Mindrinos L. The inverse scattering problem by an elastic inclusion // Advances in Computational Mathematics, 2018.-  Vol. 44.- P. 453–476.
42. Beshley A., Chapko R., Johansson B.T. An integral equation method for the numerical solution of a Dirichlet problem for second-order elliptic equations with variable coefficients // Journal of Engineering Mathematics, 2018.- Vol.112.- P.63-73.
43. Chapko R., Johansson B.T. An iterative regularizing method for an incomplete boundary data problem for the biharmonic equation // Zeitschrieft fuer Angewandte Mathematik und Mechanik, 2018.- 98.- P. 2010-2021.
44. Baravdish G. , Borachok I. , Chapko R. , Johansson B.T. , Slodička M. An iterative method for the Cauchy problem for second-order elliptic equations // International Journal of Mechanical Sciences, 2018.- 142-143.- P.216-223.
45. Chapko R., Johansson B.T. A boundary integral equation method for numerical solution of parabolic and hyperbolic Cauchy problems // Applied Numerical Mathematics, 2018.- Vol.129.-P. 104–119.
46. Chapko R., Mindrinos L. On the numerical solution of the exterior elastodynamic problem by a boundary integral equation method // Journal of Integral Equations and Applications, 2018.- 30.- P. 521-542.
47. Beshley А., Chapko R., Johansson B.T. On the alternating method and boundary-domain integrals for elliptic Cauchy problems // Computers & Mathematics with Applications.- doi.org/10.1016/j.camwa.2019.05.025 .-2019.-P.1-13.
48. Beshley A., Chapko R., Johansson B.T. A boundary domain integral equation method for an elliptic Cauchy problem with variable coefficients. In: Lindahl K., Lindström T., Rodino L., Toft J., Wahlberg P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics. Birkhäuser, Cham., 2019.- P.493-501.
49. Chapko R., Johansson B.T.,  A single-layer approach for biharmonic data completion, Proceedings of the 12th UK Conference on Boundary Integral Methods UKBIM12, Oxford Brookes University, 2019.- P.132-140.
50. Chapko R., Johansson B. T. Integral equations for biharmonic data completion // Inverse Problems and Imaging, 2019.- 13.- P.1095—1111.
51. Chapko R.S., Ivanyshyn Yaman O.M. On the non-linear integral equation method for the reconstruction of an inclusion in the elastic body // Journal of Numerical and Applied Mathematics, 2019.- 130.- P. 7—17.
52. Chapko R., Johansson B. T., Muzychuk Y., Hlova A. Wave propagation from lateral Cauchy data using a boundary element method // Wave Motion, 2019.- 91.- doi.org/10.1016/j.wavemoti.2019.102385 .- P.1-12.
53. Chapko R., Johansson B.T., Mindrinos L. On a boundary integral solution of a lateral planar Cauchy problem in elastodynamics // Journal of Computational and Applied Mathematics, 2019.- doi.org/10.1016/j.cam.2019.112463.-P.1-16.
54. Chapko R., Mindrinos L. On the non-linear integral equation approach for an inverse boundary value problem for the heat equation // Journal of Engineering Mathematics, 2019.- doi.org/10.1007/s10665-019-10028-4.-P.1-16.
55. Borachok I., Chapko R., Johansson B.T. A method of fundamental solutions for heat and wave propagation from lateral  Cauchy data // Numerical  Algorithms. Springer. – 2021. – P. 1-19 (DOI: 10.1007/s11075-021-01120-x). 

56. Chapko R., Johansson B.T., Shtoyko M. A double-layer potential approach for planar Cauchy problems for the Laplace equation // Вісник Львівського університету. Серія прикладна математика та інформатика. – 2020. – Вип. 28. – P. 15-26 (DOI: 10.30970/vam.2020.28.10980).

57. Borachok I., Chapko R., Johansson B.T.  A method of fundamental solutions with time-discretisation for wave motion from lateral Cauchy data // Partial Differential Equations and Applications. – 2022. – Vol.3, №37 – P. 1-13 (DOI:10.1007/s42985-022-00177-0).

58. Chapko R., Johansson B.T., Vlasiuk M.Boundary integrals for data reconstruction on an elastostatic crack // International Journal of Applied and Computational Mathematics. – 2022. – Vol.40, №8 – P. 1-18 (DOI: 10.1007/s40819-021-01232-x).
59. Chapko R., Johansson B.T. Calculating heat and wave propagation from lateral Cauchy data // Український математичний журнал. – 2022. – Vol.74, №2 – P. 274-285. (DOI: 10.37863/umzh.v74i2.6880).
60. Chapko R., Mindrinos L. On the numerical solution of a hyperbolic inverse boundary value problem in bounded domains // Mathematics. – 2022. – Vol.750, №10 – P. 1-11 (DOI: 10.3390/math10050750).
61. Borachok I., Chapko R., Johansson B.T. An inverse elastodynamic data reconstruction // Journal of Engineering Mathematics. – 2022. – Vol.134, №3 – P. 1-13 (DOI: 10.1007/s10665-022-10219-6).

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Отримав Державну премію України в галузі науки і техніки за 2012р в складі колективу авторів за цикл наукових праць «Дискретні та функціональні методи теорії наближення та їх застосування».

Силабуси навчальних дисциплін для слухачів освітньо-наукових програм підготовки доктора філософії:

• Науковий семінар
• Педагогічна практика
• Методологія підготовки наукової публікації

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