Roman Chapko

Position: Chairperson, Computational Mathematics Department

Scientific degree: Doctor of Physical and Mathematical Sciences

Academic status: Professor

Email: chapko@lnu.edu.ua

Research interests

Numerical solution of the integral equation of the first kind with logarithmic- or hyper-singularity. Numerical solution of initial boundary value problems using of integral equation method. Numerical solution of inverse problems for heat equation.

Courses

Selected publications

  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.- DOI: 10.1080/17415977.2013.829467.-P.1-20.
  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.- DOI: 10.1515/jiip-2015-0053.- P.1-15.
  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.- DOI: 10.1080/17415977.2015.1130042.- P. 1-19.
  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, 2016.-  DOI: 10.1007/s10665-016-9858-6.- P.1-17.
  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 // Журнал обчислювальної та прикладної математики, 2016.- Вип. 122.- С.7-20.
  39. Chapko R., Johansson B.T. A boundary integral approach for numerical solution of the Cauchy problem for the Laplace equation // Український математичний журнал, 2016.- т. 68.- № 12.- C.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 // Журнал обчислювальної та прикладної математики, 2017.- Вип. 126.- С.1632.
  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.- DOI: 10.1002/zamm.201800102.- P.1-12.
  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.- Vol. 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.

Scientific biography

EDUCATION

2005
Doctor of Science in Computational Mathematics, graduated 2005. Dissertation “Numerical solution of linear direct and nonlinear inverse evolution problems”.
1998-1999
Kyiv National University (Ukraine). Postdoctoral research in Faculty of Cybernetic.
1985-1989
Lviv National University (Ukraine). Doctoral studies in Faculty of Applied Mathematics and Mechanic. Ph.D. in Computational Mathematics, graduated Spring 1990. Advisor: Professor Iosyf Lyudkevych. Dissertation: “Numerical solution of initial boundary value problems for telegraph equation in the case of open surfaces”.
1980-1985
Lviv National University. Studies in Faculty of Applied Mathematics and Mechanic. Dipl. (equivalent to M.S.) in Applied Mathematics. Advisor: Professor Iosyf Lyudkevych

PERSONAL DATA

Ukrainian citizen, married, two children. Place and date of birth : Kulchyci (near Lviv) October 26, 1963.

HONORS AND AWARDS

1998
Universität Göttingen. Researcher in DFG project for six months. Leader: Professor Rainer Kreß

 

1997-1998
Universität Göttingen. KAAD fellowship (Germany) for ten months.
1995-1996
Universität Göttingen. DAAD fellowship (Germany) for three months. Advisor: Professor Rainer Kreß.
1992
Universität Stuttgart. DAAD fellowship (Germany) for six months. Advisor: Professor Wolfgang Wendland.
1991-1992
Universität Göttingen. DAAD fellowship (Germany) for six months. Advisor: Professor Rainer Kreß.

PROFESSIONAL APPOINTMENTS

2000 – present
Lviv National University, Head of Department of Computational Mathematics.
1999-2000
1993-1997
Lviv National University, Faculty of Applied Mathematics and Computer Sciences, Dozent, Department of Computational Mathematics.
1989-1993
Lviv National University, Assistant, Department of Computational Mathematics.

RESEARCH INTEREST

Numerical solution of the integral equation of the first kind with logarithmic- or hyper-singularity. Numerical solution of initial boundary value problems using of integral equation method. Numerical solution of inverse problems for heat equation.

TEACHING INTEREST

Numerical solution of ordinary differential equations. Numerical solution of partial differential equations. Numerical and engineering mathematics in applied sciences.

SPECIAL SKILLS

Bilingual in Ukrainian and Russian, good knowledge of German and Polish, satisfactory in English. Experienced in Fortran, Pascal, Unix, Windows NT – Seven, LaTEX, MatLab and Mathematica.

THESIS DIRECTED

1996
A. Pereymybida, “Numerical solution of initial boundary value problems for telegraph equation by potentials method”. Ph.D. thesis (Computational Mathematics).
2009
G. Datsiv, “Numerical solution the axisymmetric linear sloshing problems by the integral equation method”.Ph.D. thesis (Computational Mathematics).
2010

 

N. Lytovchenko, “Numerical solution of inverse boundary value problems of potential theory in semi-infinite regions with using boundary integral equations”. Ph.D. thesis (Computational Mathematics).
2013
VVavrychyk, Iterative methods based on integral equations for numerical solution of a Cauchy problem for the parabolic equation“.D. thesis (Computational Mathematics).
2015
Yu. Muzychuk, “Numerical solution of boundary value problems for some infinite triangular systems of elliptic equations”. Ph.D. thesis (Computational Mathematics).

Awards

Received the State Prize of Ukraine in Science and Technology in 2012 as a part of a group of authors for a series of scientific papers “Discrete and functional methods of approximation theory and its application.”

Schedule