Karolina Kropielnicka

My current interests:

• Interpolation in a simplex
• Computations for highly oscillatory problems
• Asymptotic expansions in computational mathematics
• Approximation on unbounded domains
• Numerical computations in quantum mechanics
• Composition and decomposition methods
• Structured population models
• Particle methods (EBT, pseudo-particle methods)
• Numerical methodologies in spaces of measures

List of publications:

1. A. Iserles, K. Kropielnicka, An elementary approach to splittings of unbounded operators, submitted, https://arxiv.org/abs/2401.06635,


2. J. C. del Valle, K. Kropielnicka, Family of Strang-type exponential splittings in the presence of unbounded and time dependent operators, submitted, https://doi.org/10.48550/arXiv.2310.01556,


3. K. Kropielnicka, K. Lademann, K. Schratz, Effective high order integrators for low to highly oscillatory Klein-Gordon equations, submitted, https://doi.org/10.48550/arXiv.2112.08908,


4. K. Kropielnicka, R. Perczynski, Asymptotic expansions for the linear PDEs with oscillatory input terms; Analytical form and error analysis, Computers and Mathematics with Applications, 156 (2024), 1627, https://doi.org/10.1016/j.camwa.2023.12.012,


5. K. Kropielnicka, K. Lademann, Third-order exponential integrator for linear Klein-Gordon equations with time- and space dependent mass, https://arxiv.org/pdf/2212.13762.pdf,ESAIM: Mathematical Modelling and Numerical Analysisa, 57 (2023), no. 6, 34833498, https://doi.org/10.1051/m2an/2023087,


6. A. Iserles, K. Kropielnicka, K. Schratz, M. Webb, Solving the linear Schrödinger equation on the real line, http://arxiv.org/abs/2102.00413 (2021)


7. M. Condon, K. Kropielnicka, K. Lademann, R. Perczyski , Asymptotic numerical solver for the linear Klein-Gordon equation with space- and time-dependent mass, Appl. Math. Lett., 115:106935, 7, (2021)


8. W. Auzinger, J. Dubois, K. Held, H. Hofstätter, T. Jawecki, A. Kauch, O. Koch, K. Kropielnicka, P. Singh, C. Watzenböck, Efficient Magnus-type integrators for solar energy conversion in Hubbard models, , Journal of Computational Mathematics and Data Science , 2(100018), 100018. (2022), https://doi.org/10.1016/j.jcmds.2021.100018 , arXiv:2104.02034v1


9. M. Condon, A. Iserles, K. Kropielnicka, P. Singh, Solving the wave equation with multifrequency oscillations, Journal of Computational Dynamics, 6, no 2, pp. 239-249, (2019) doi:10.3934/jcd.2019012


10. W. Auzinger, H. Hofstätter, O. Koch, K. Kropielnicka, P. Singh, Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime, Appl. Math. Comput. 362 (2019), 124550, 10 pp., arXiv:1902.04324v1
    


11. J. A. Carrillo, P. Gwiazda, K. Kropielnicka, A. Marciniak-Czochra, The escalator boxcar train method for a system of aged-structured equations in the space of measures, SIAM J. Numer. Anal. 57 (2019), no. 4, 1842-1874., arXiv:1806.01770v1


12. A. Iserles, K. Kropielnicka, P. Singh, Solving Schrödinger equation in semiclassical regime with highly oscillatory time-dependent potentials, J. Comput. Phys. 376 (2019), 564-584. https://doi.org/10.1016/j.jcp.2018.09.047
    


13. A. Iserles, K. Kropielnicka, P. Singh, Compact schemes for laser matter interaction in Schrödinger equation based on effective splittings of Magnus expansion, Computer Physics Communications 234, (2019) 195-201, https://doi.org/10.1016/j.cpc.2018.07.010
    


14. A. Iserles, K. Kropielnicka, P. Singh, Magnus Lanczos methods with simplified commutators for the Schrödinger Equation with a time-dependent potential. SIAM J. Numer. Anal. 56 (2018), no. 3, 1547-1569.


15. Bader, P., Iserles, A., Kropielnicka, K. & Singh, P., Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential. Proc. A. 472 (2016), no. 2193, 20150733, 18 pp.


16. P. Gwiazda, K. Kropielnicka, A. Marciniak-Czochra, The escalator boxcar train method for a system of age-structured equations, Netw. Heterog. Media, 11 (2016), no.1, 123-143, arXiv:1506.00016v2


17. P. Bader, A. Iserles, K. Kropielnicka, P. Singh, Effective approximation for the semiclassical Schrödinger equation, Found. Comp. Maths, 14 (2014), no. 4, 689-720


18. M. Condon, A. Deano, A. Iserles, K. Kropielnicka, Efficient computation of delay differential equations with highly oscillatory terms, ESAIM Math. Model. Numer. Anal., 46, (2012), no. 6, 1407-1420


19. Z. Kamont, K. Kropielnicka, Implicit difference methods for evolution functional differential equations, Numerical Analysis and Applications, 4, (2011), no. 4, 294-308


20. Z. Kamont, K. Kropielnicka, Comparison of explicit and implicit difference schemes for parabolic functional differential equations, Ann. Polon. Math. 103, (2012), 135-160


21. K. Kropielnicka, L. Sapa, Estimate of solutions for differential and difference functional equations with applications to difference methods, Appl. Math. Comput., 217, (2011), no. 13, 6206-6218


22. K. Kropielnicka, Implicit difference methods for parabolic PDE on cylindrical domains, Dynamic Systems and Applications, 19, (2010), 557-576


23. Z. Kamont, K. Kropielnicka, Numerical method of lines for parabolic functional differential equations, Applicable Analysis, 88, (2009), no. 12, 1631-1650


24. Z. Kamont, K. Kropielnicka, Implicit difference functional inequalities corresponding to first-order partial differential functional equations, Journal Of Applied Mathematics and Stochastic Analysis, (2009), Article ID 245720


25. Z. Kamont, K. Kropielnicka, Implicit difference functional inequalities and applications, Journal Of Mathematical Inequalities, 2, (2008), no. 3, 407-427


26. K. Kropielnicka, Implicit difference methods for quasilinear parabolic functional differential problems of the Dirichlet type, Applicationes Mathematicae, 35, (2008), no.2, 155-175.


27. K. Kropielnicka, Implicit difference methods for parabolic functional differential problems of the Neumann type, Nonlinear Oscillations, 11, (2008), no. 3, 329-347


28. K. Kropielnicka, Implicit difference methods for quasilinear parabolic functional differential systems, Univ. Iagel. Acta Math., 45, (2007), 175-195


29. K. Kropielnicka, Stability of implicit difference equations generated by parabolic functional differential problems, Computational Methods in Applied Mathematics, 7, (2007), no.1, 68-82


30. K. Kropielnicka, Difference methods for parabolic functional differential problems of the Neumann type, Ann. Polon. Math., 92, (2007), no. 2, 163-178


31. K. Kropielnicka, Convergence of implicit difference methods for parabolic functional differential equations, Int. Journal of Math. Analysis, 1, (2007), no. 6, 257-277


32. K. Kropielnicka, Implicit difference method for nonlinear parabolic functional differential systems, Dem. Math., 39, (2006), no.3, 711-728


33. K. Kropielnicka, Implicit difference method for parabolic functional differential equations, Funct. Diff. Equat., 13, (2006), no.3-4, 483-510


34. K. Kropielnicka, Numerical method of bicharacteristic for quasilinear hyperbolic functional differential systems, Comment. Math., 45, (2005), no.1, 91-109


35. Z. Kamont, K. Kropielnicka, Differential difference inequalities related to hyperbolic functional differential systems and applications, Math. Ineq. a. Appl., 8, (2005), no.4, 655-674