Αριθμητική επίλυση διαφορικών εξισώσεων με μεθόδους απλού βήματος Runge-Kutta, Runge-Kutta-Nyström, Partitioned Runge-Kutta, Two-Derivative Runge-Kutta και πολλαπλού βήματος τύπου Numerov. Εφαρμογή σε χαμιλτονιανά προβλήματα και προβλήματα με ταλαντωτική ή περιοδική συμπεριφορά της λύσης. Μέθοδοι με συγκεκριμένες ιδιότητες όπως εκθετικά και τριγωνομετρικά προσαρμοσμένες μέθοδοι, συμπλεκτικές μέθοδοι, μέθοδοι με ελάχιστη υστέρηση φάσης και με ελάχιστο σφάλμα μεγέθυνση.
Ενδεικτικά προβλήματα εφαρμογής: το πρόβλημα δύο σωμάτων, το διαταραγμένο (perturbed) πρόβλημα δύο σωμάτων, ο διπλός αρμονικός ταλαντωτής, το απλό εκκρεμές, το τροχιακό πρόβλημα Stiefel και Bettis, σύστημα μη γραμμικών ταλαντωτών, η εξίσωση του Schrödinger.

Ζαχαρούλα Καλογηράτου
Θεόδωρος Μονοβασίλης
Δημοσιεύσεις
1. Williams, Z. Kalogiratou, Best Chebyshev approximation from families of ordinary differential equations, IMA Journal Numerical Analysis, 13 (1993) 383‐395.
2. J. Williams, Z. Kalogiratou, Nonlinear Chebyshev fitting from the solution of ordinary differential equations, Numerical Algorithms, 5 (1993) 325‐337.
3. J. Williams, Z. Kalogiratou, Least squares and Chebyshev fitting for parameterestimation in ODEs, Advances in Computational Mathematics, 1(1993) 357‐366.
4. Z. Kalogiratou, T.E. Simos, A P‐stable Exponentially‐Fitted Method for the Numerical Integration of the Schrödinger Equation, Applied Mathematics and Computation, 112 (2000) 99‐112.
5. Z. Kalogiratou, T.E. Simos, Construction of trigonometrically and exponentially‐fitted Runge‐Kutta‐Nystrom methods – a method of 8th algebraic order, Journal of Mathematical Chemistry, 31 (2002) 211‐232.
6. Z. Kalogiratou, T.E. Simos, Newton‐Cotes Formulae for Long Time Integration, Journal of Computational and Applied Mathematics, 158 (2003).
7. Z. Kalogiratou, Th. Monovasilis, T.E. Simos, Symplectic integrators for the numerical solution of the Schrödinger equation, Journal of Computational and Applied Mathematics, 158 (2003) 83‐92.
8. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Numerical Solution of the twodimensional time‐ independent Schrödinger Equation by Symplectic Schemes, Applied Numerical Analysis and Computational Mathematics (ANACM), 1 (2004) 195‐204.
9. Z. Kalogiratou, Th. Monovasilis, T.E. Simos, Numerical solution of the Two‐Dimensional time‐independent Schrödinger equation with exponential‐fitting methods, Journal of Mathematical Chemistry, 37(2005) 271‐279.
10. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Exponential‐ fitting symplectic methods for the numerical integration of the Schrödinger equation, Journal of Mathematical Chemistry, 37 (2005) 263‐270.
11. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Trigonometrically and Exponentially fitted Symplectic Methods of third order for the numerical integration of the Schrödinger equation, Applied Numerical Analysis and Computational Mathematics (ANACM), 2 (2005)238‐244.
12. Z. Kalogiratou, Th. Monovasilis, T.E. Simos, A Symplectic Trigonometrically Fitted Modified Partitioned Runge‐Kutta Method for the Numerical Integration of Orbital Problems, Applied Numerical Analysis and Computational Mathematics (ANACM), 2 (2005) 359‐364.
13. Z. Kalogiratou, Th. Monovasilis, and T.E. Simos, Computation of the eigenvalues of the one‐dimensional Schrödinger equation by symplectic methods, International Journal of Quantum Chemistry, 106 (2006) 795‐802.
14. Kalogiratou Z., Symplectic Trigonometrically fitted Partitioned Runge‐Kutta methods, Physics Letters A, 370 (2007) 1‐7.
15. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation, Journal of Mathematical Chemistry, 40 (2006) 257‐267.
16. Th. Monovasilis, and T.E. Simos, Symplectic and Trigonometrically fitted Symplectic methods of second and third order, Physics Letters A, 354 (2006) 377-383.
17. Th. Monovasilis, and T.E. Simos, Symplectic methods for the numerical integration of the Schrödinger equation, Computational Materials Science, 38 (2007) 526-532.
18. Th. Monovasilis, and T.E. Simos, New Second-Order Exponentially and Trigonometrically Fitted Symplectic Integrators for the Numerical Solution of the Time-independent Schrödinger Equation, Journal of Mathematical Chemistry, 42 (2007) 535-545.
19. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Families of Third and Fourth Algebraic Order Trigonometrically Fitted Symplectic Methods for the Numerical Integration of Hamiltonian Systems, Computer Physics Communications, 177 (2007) 757‐763.
20. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Computation of the eigenvalues of the Schrödinger equation by symplectic and trigonometrically fitted symplectic partitioned Runge‐Kutta methods, Physics Letters A, 372 (2008) 569‐573.
21. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, A family of trigonometrically fitted partitioned Runge–Kutta symplectic methods, Applied Mathematics and Computation, 209 (2009) 91‐96.
22. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Computation of the eigenvalues of the Schrödinger equation by exponentially‐fitted Runge–Kutta–Nyström methods, Computer Physics Communications, 180 (2009) 167‐176.
23. Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Symplectic Partitioned Runge–Kutta methods with minimal phase‐lag, Computer Physics Communications, 181 (2009) 1251‐1254.
24. Z. Kalogiratou, Th. Monovasilis and T.E. Simos Modified Runge‐Kutta‐Nystrom Methods for the Numerical Integration of Schrodinger Equation, Computers and Mathematics with Applications. 60 (2010) 1639‐1647.
25. Th. Monovasilis, Z. Kalogiratou and T.E. Simos, Two new phase‐fitted symplectic partitioned Runge Kutta methods, International Journal of Modern Physics C, 22, 12, (2011) 1343‐1355.
26. Th. Monovasilis, Symplectic Partitioned Runge-Kutta methods with the phase-lag property, Applied Mathematics and Computation, 218 (2012) 9075-9084.
27. Th. Monovasilis, Phase fitted Symplectic Partitioned Runge-Kutta methods for the numerical integration of the Schrodinger equation, Journal of Mathematical Chemistry, 50 (2012) 1736–1746
28. Th. Monovasilis, Z. Kalogiratou and T.E. Simos, Exponentially Fitted Symplectic Runge‐Kutta‐Nystrom methods, Applied Mathematics & Information Sciences (AMIS), 7 (2013) 81‐85.
29. Z. Kalogiratou, Th. Monovasilis, G. Psihoyios, T.E. Simos, Runge–Kutta type methods with special properties for the numerical integration of ordinary differential equations, Physics Reports, 536 (2014) 75‐146.
30. Z. Kalogiratou, Th. Monovasilis, Diagonally Implicit Symplectic Runge‐Kutta methods with special properties, Applied Mathematics & Information Sciences (AMIS), 9 (2015) 11-17.
31. Z. Kalogiratou, Th. Monovasilis, T.E. Simos, A fourth order modified trigonometrically fitted symplectic Runge–Kutta–Nyström method, Computer Physics Communications, 185 (2014) 3151‐3155.
32. Th. Monovasilis Z. Kalogiratou and T.E. Simos, Construction of exponentially fitted symplectic Runge‐Kutta‐Nystrom methods from Partitioned Runge‐Kutta methods, Applied Mathematics & Information Sciences (AMIS), 9 (2015) 1923‐1930.
33. Z. Kalogiratou, Th. Monovasilis and T.E. Simos, Symplectic Runge‐Kutta‐Nystrom Methods with phase‐lag order 8 and infinity, Applied Mathematics & Information Sciences (AMIS), 9 (2015) 1105‐1112.
34. Th. Monovasilis Z. Kalogiratou and T.E. Simos, Construction of Exponentially Fitted Symplectic Runge–Kutta–Nyström Methods from Partitioned Runge–Kutta Methods, Mediterranean Journal of Mathematics, 13 (2015) 2271‐2285.
35. Higinio Ramos, Z. Kalogiratou, Th. Monovasilis,∙T. E. Simos, An optimized two‐step hybrid block method for solving general second order initial‐value problems, Numerical Algorithms, 72 (2016) 1089‐1102.
36. Z. Kalogiratou, Th. Monovasilis, Higinio Ramos, T. E. Simos, A new approach on the construction of trigonometrically fitted two step hybrid methods, Journal of Computational and Applied Mathematics, 303 (2016) 146‐155.
37. Th. Monovasilis, Z. Kalogiratou, Higinio Ramos, T. E. Simos, Modified two‐step hybrid methods for the numerical integration of oscillatory problems, Mathematical Methods in the Applied Sciences, 40(14), (2017) 5286‐5294.
38. Th. Monovasilis, Z. Kalogiratou,∙T. E. Simos, Trigonometrical fitting conditions for two derivative Runge‐Kutta methods, Numerical Algorithms, 79(3), (2018) 787‐800.
39. Z. Kalogiratou, Th. Monovasilis, T. E. Simos, New fifth order Two‐Derivative Runge‐Kutta methods with constant and frequency dependent coefficients, Mathematical Methods in the Applied Sciences, 42(6), (2019), 1955‐1966.
40. Z. Kalogiratou, Th. Monovasilis, T. E. Simos, Two‐derivative Runge‐Kutta methods with optimal phase properties, Mathematical Methods in the Applied Sciences 43 (2020) 1267‐1277.