My reasearch


Research interests

  • Dynamical systems
  • Computer Assisted Proofs
  • Numeric computations, computer simulation
  • Rigorous integration of Delay Differential Equations
  • Molecular simulation
  • Bioinformatics

Scholarships and grants


From newer to older

  1. Szczelina, R.; Baczyński, K.; Markiewicz, M.; Pasenkiewicz-Gierula, M.; Network of lipid interconnections at the interfaces of galactolipid and phospholipid bilayers, Journal of Molecular Liquids, Accepted (2019), In Press, [doi:10.1016/j.molliq.2019.112002]

  2. Plesnar, E.; Szczelina, R.; Subczynski, K.W.; Pasenkiewicz-Gierula, M.; Is the cholesterol bilayer domain a barrier to oxygen transport into the eye lens?, Biochimica et Biophysica Acta (BBA) - Biomembranes (2018), Vol. 1860, Iss. 2, Pages 434–441, [doi:10.1016/j.bbamem.2017.10.020]

  3. Szczelina, R.; Zgliczyński, P.; Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation, Foundations of Computational Mathematics (2018), Vol. 18, Iss 6, Pages 1299--1332, [Open Access, doi:10.1007/s10208-017-9369-5] [arxiv preprint]

    Source codes available here

  4. Szczelina, R. A computer assisted proof of multiple periodic orbits in some first order non-linear delay differential equation, Electronic Journal of Qualitative Theory of Differential Equations (2016), No. 83, 1-19, [Open Access, doi:10.14232/ejqtde.2016.1.83] [PDF]

    Source codes available here

  5. Szczelina, R. Murzyn, K. DMG-α-A Computational Geometry Library for Multimolecular Systems, Journal of Chemical Information and Modeling (2014), 54 (11), 3112–3123 [doi:10.1021/ci500273s]

    Work founded under Polish National Science Center (NCN) grant no. 2011/01/N/ST6/07173. [project homepage - documentation]

  6. Szczelina, R. Zgliczyński, P. A Homoclinic Orbit in a Planar Singular ODE---A Computer Assisted Proof, SIAM Journal of Applied Dynamical Systems 12 (2013), 1541-–1565 [doi:10.1137/120901271] [preprint (PDF)]

    Source codes (compiling instructions inside):

    • no MSYS (CAPD 2.0): [zip]
    • with MSYS (CAPD 3.0): [zip]
    • Compatible with MSYS, installation of CAPD 3.0 required : [zip]


  1. SocBiN / BIT Bioinformatics, June 26 - June 29, 2013 Toruń, Poland

    Poster: Lipid bilayer analysis using 3D Voronoi diagrams [poster in .PDF]

  2. The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 07 - July 11, 2014 Madrid, Spain

    Talk: Rigorous integration of Delay Differential Equations [presentation in .PDF]

  3. BIO 2014 Congress, September 9 - September 12, 2014 Warsaw, Poland

    Poster: DMG-α: computational geometry package for analysis of molecular dynamic simulations [poster in .PDF]

  4. Short Thematic Program on Delay Differential Equations: Differential equations with variable delay, May 04 – May 08, 2015 Fields Institute, Toronto, Canada

    Invited talk: Rigorous integration of DDEs and applications

  5. Dynamics, Topology and Computations (DyToComp), June 15 – June 20, 2015 Banach Center of IMPAN, Będlewo, Poland

    Talk: Rigorous integration of delay differential equations and applications

  6. 10th Colloquium on the Qualitative Theory of Differential Equations, July 01 – July 04, 2015 Szeged, Hungary

    Talk: Constructing Poincaré maps for delay differential equations using rigorous interval arithmetic

  7. 19th IUPAB congress and 11th EBSA congress, July 16 – July 20, 2017 Edinburgh, Scotland/United Kingdom

    Poster: Computational study of oxygen transport across domains of the membrane of the eye lens fibre cells

  8. Dynamics, Topology and Computations (DyToComp), June 18 - June 23, 2018 IMPAN Banach Center, Będlewo, Poland

    Talk: Some developments in rigorous forward in time integration of Delay Differential Equations

  9. 11th Colloquium on the Qualitative Theory of Differential Equations, June 17 – June 21, 2019 Szeged, Hungary

    Talk: Some improvements in rigorous integration of Delay Differential Equations

  10. Jubileuszowy Zjazd Matematyków Polskich w stulecie PTM, september 3 - september 7, 2019 UJ / AGH, Krakow, Poland

    Talk: Ścisłe całkowanie równań różniczkowych z opóźnieniem