Link to DORA (De Montfort Open Research Archive)
https://www.dora.dmu.ac.uk/browse?type=author&value=Anastassi%2C+Zacharias
Recent Publications

Anastassi, Zacharias; Kosti, Athinoula A.; Rufai, Mufutau Ajani (Article)We investigate the numerical solution of the nonlinear Schrödinger equation in two spatial dimensions and one temporal dimension. We develop a parametric Runge–Kutta method with four of their coefficients considered as ...

ColreavyDonnelly, S.; Kuhn, Stefan; Caraffini, Fabio; O'Connor, S.; Anastassi, Zacharias; Coupland, Simon (Conference)This study combines two novel deterministic methods with a Convolutional Neural Network to develop a machine learning method that is aware of directionality of light in images. The first method detects shadows in terrestrial ...

Bielby, James; Kuhn, Stefan; ColreavyDonnelly, S.; Caraffini, Fabio; O'Connor, S.; Anastassi, Zacharias (Conference)Developments in artificial intelligence can be leveraged to support the diagnosis of degenerative disorders, such as epilepsy and Parkinson’s disease. This study aims to provide a software solution, focused initially towards ...

Kosti, Athinoula; ColreavyDonnelly, S.; Caraffini, Fabio; Anastassi, Zacharias (Article)Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrödinger equation with timedependent coefficients, we develop a modified RungeKutta pair with improved ...

Anastassi, Zacharias; Fotopoulos, G.; Frantzeskakis, D. J.; Horikis, T. P.; Karachalios, N. I.; Kevrekidis, P. G.; Stratis, I. G.; Vetas, K. (Article)We consider the asymptotic behavior of the solutions of a nonlinear Schrödinger (NLS) model incorporating linear and nonlinear gain/loss. First, we describe analytically the dynamical regimes (depending on the gain/loss ...

Tsitoura, F.; Anastassi, Zacharias; Marzuola, J. L.; Kevrekidis, P. G.; Frantzeskakis, D. J. (Article)Motivated by the recent theoretical study of (bright) soliton diode effects in systems with multiple scatterers, as well as by experimental investigations of solitonimpurity interactions, we consider some prototypical ...

Tsitoura, F.; Anastassi, Zacharias; Marzuola, J. L.; Kevrekidis, P. G.; Frantzeskakis, D. J. (Article)We study dark solitons near potential and nonlinearity steps and combinations thereof, forming rectangular barriers. This setting is relevant to the contexts of atomic BoseEinstein condensates (where such steps can be ...

Anastassi, Zacharias; Kosti, A. A. (Article)In this paper an optimization of the nonFSAL embedded RKN 6(4) pair with six stages of Moawwad ElMikkawy, ElDesouky Rahmo is presented. The new method is derived after applying phasefitting and amplificationfitting ...

Kosti, A. A.; Anastassi, Zacharias (Article)In this paper, three families of explicit Runge–Kutta–Nyström methods with three stages and third algebraic order are presented. Each family consists of one method with constant coefficients and one corresponding optimized ...
All Publications in Refereed Journals
P39. Z.A Anastassi, A.A. Kosti, M.A. Rufai, A Parametric Method Optimised for the Solution of the (2+1)Dimensional Nonlinear Schrödinger Equation, Mathematics, 11, 609 (2023).
P38. A.A. Kosti, S. ColreavyDonnelly, F. Caraffini, Z.A. Anastassi, Efficient Computation of the Nonlinear Schrödinger Equation with TimeDependent Coefficients, Mathematics, 8, 374 (2020).
P37. F. Tsitoura, Z.A. Anastassi, J.L. Marzuola, P.G. Kevrekidis, and D.J. Frantzeskakis, Dark Soliton Scattering in Symmetric and Asymmetric Double Potential Barriers, Physics Letters A, 381, 31, 25142520 (2017).
P36. Z.A. Anastassi, G. Fotopoulos, D.J. Frantzeskakis, T.P. Horikis, N.I. Karachalios, P.G. Kevrekidis, I.G. Stratis, and K. Vetas, Spatiotemporal algebraically localized waveforms for a nonlinear Schrödinger model with gain and loss, Physica D, 355, 2433 (2017).
P35. F. Tsitoura, Z.A. Anastassi, J.L. Marzuola, P.G. Kevrekidis, and D.J. Frantzeskakis, Dark solitons near potential and nonlinearity steps, Physical Review A, 94, 063612 (2016).
P34. Z.A. Anastassi, A.A. Kosti, A 6(4) Optimized Embedded RungeKuttaNyström Pair for the Numerical Solution of Periodic Problems, Journal of Computational and Applied Mathematics, 275, 311320 (2015).
P33. A.A. Kosti, Z.A. Anastassi, Explicit Almost PStable RungeKuttaNyström Methods for the Numerical Solution of the TwoBody Problem, Computational and Applied Mathematics, 34, 2, 647659 (2015).
P32. G.A. Panopoulos, Z.A. Anastassi, T.E. Simos, A New EightStep Symmetric Embedded PredictorCorrector Method (EPCM) for Orbital Problems and Related IVPs with Oscillatory Solutions, The Astronomical Journal, 145, 75 (2013).
P31. Z.A. Anastassi, T.E. Simos, A parametric symmetric linear fourstep method for the efficient integration of the Schrödinger equation and related oscillatory problems, Journal of Computational and Applied Mathematics, 236, 16, 38803889 (2012).
P30. I. Alolyan, Z.A. Anastassi, T.E. Simos, A New Family of Symmetric Linear FourStep Methods for the Efficient Integration of the Schrödinger Equation and Related Oscillatory Problems, Applied Mathematics and Computation, 218, 9, 53705382 (2012).
P29. A.A. Kosti, Z.A. Anastassi, T.E. Simos, An optimized explicit RungeKuttaNyström method for the numerical solution of orbital and related periodical initial value problems, Computer Physics Communications, 183, 3, 470479 (2011).
P28. A.A. Kosti, Z.A. Anastassi, T.E. Simos, Construction of an optimized explicit RungeKuttaNyström method for the numerical solution of oscillatory initial value problems, Computers and Mathematics with Applications, 61, 11, 33813390 (2011).
P27. G.A. Panopoulos, Z.A. Anastassi, T. E. Simos, A Symmetric EightStep PredictorCorrector Method for the Numerical Solution of the Radial Schrödinger Equation and related IVPs with oscillating solutions, Computer Physics Communications, 182, 8, 16261637 (2011).
P26. Z.A. Anastassi, A new symmetric linear eightstep method with fifth trigonometric order for the efficient integration of the Schrödinger equation, Applied Mathematics Letters, 24, 8, 14681472 (2011).
P25. G.A. Panopoulos, Z.A. Anastassi, T. E. Simos, A New Symmetric EightStep PredictorCorrector Method for the Numerical Solution of the Radial Schrödinger Equation and Related Orbital Problems, International Journal of Modern Physics C, 22, 2, 133153 (2011).
P24. D.F. Papadopoulos, Z.A. Anastassi, T.E. Simos, An optimized RungeKuttaNyström method for the numerical solution of the Schrödinger equation and related problems, MATCH Commun. Math. Comput. Chem., 64, 2, 551566 (2010).
P23. D.F. Papadopoulos, Z.A. Anastassi, T.E. Simos, A modified phasefitted and amplificationfitted RungeKuttaNyström method for the numerical solution of the radial Schrödinger equation, Journal of Molecular Modeling, 16, 8, 13391346 (2010).
P22. A.A. Kosti, Z.A. Anastassi, T.E. Simos, An optimized explicit RungeKutta method with increased phaselag order for the numerical solution of the Schrödinger equation and related problems, Journal of Mathematical Chemistry, 47, 1, 315330 (2010).
P21. Z.A. Anastassi and T.E. Simos: Numerical Multistep Methods for the Efficient Solution of Quantum Mechanics and Related Problems, Physics Reports, vol. 482483, pp. 1240 (2009).
P20. D.F. Papadopoulos, Z.A. Anastassi, T.E. Simos, A PhaseFitted RungeKuttaNyström method for the Numerical Solution of Initial Value Problems with Oscillating Solutions, Computer Physics Communications, 180, 10, 18391846 (2009).
P19. D.S. Vlachos, Z.A. Anastassi, T.E. Simos, High order phase fitted multistep integrators for the Schrödinger equation with improved frequency tolerance, Journal of Mathematical Chemistry, 46, 4, 10091049 (2009).
P18. D.S. Vlachos, Z.A. Anastassi, T.E. Simos, High order multistep methods with improved phaselag characteristics for the integration of the Schrödinger equation, Journal of Mathematical Chemistry, 46, 2, 692725 (2009).
P17. Z.A. Anastassi, D.S. Vlachos, T. E. Simos, A new methodology for the construction of numerical methods for the approximate solution of the Schrödinger equation, Journal of Mathematical Chemistry, 46, 2, 652691 (2009).
P16. Z.A. Anastassi, D.S. Vlachos, T. E. Simos, A new methodology for the development of numerical methods for the numerical solution of the Schrödinger equation, Journal of Mathematical Chemistry, 46, 2, 621651 (2009).
P15. D.S. Vlachos, Z.A. Anastassi, T.E. Simos, A New Family of Multistep Methods with Improved Phase Lag Characteristics for the Integration of Orbital Problems, The Astronomical Journal, 138, 8694 (2009).
P14. G.A. Panopoulos, Z.A. Anastassi, T. E. Simos, Two optimized symmetric eightstep implicit methods for initialvalue problems with oscillating solutions, Journal of Mathematical Chemistry, 46, 2, 604620 (2009).
P13. Z.A. Anastassi, D.S. Vlachos, T. E. Simos, A family of RungeKutta methods with zero phaselag and derivatives for the numerical solution of the Schrödinger equation and related problems, Journal of Mathematical Chemistry, 46, 4, 11581171 (2009).
P12. Z.A. Anastassi and T.E. Simos: A family of twostage twostep methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution, Journal of Mathematical Chemistry, 45, 4, 11021129 (2009).
P11. Z.A. Anastassi and T.E. Simos: A SixStep Pstable TrigonometricallyFitted Method for the Numerical Integration of the Radial Schrödinger Equation, MATCH Commun. Math. Comput. Chem., 60, 3, 803830 (2008).
P10. G.A. Panopoulos, Z.A. Anastassi and T.E. Simos: Two New Optimized EightStep Symmetric Methods for the Efficient Solution of the Schrödinger Equation and Related Problems, MATCH Commun. Math. Comput. Chem., 60, 3, 773785 (2008).
P9. T.V. Triantafyllidis, Z.A. Anastassi and T.E. Simos: Two Optimized RungeKutta Methods for the Solution of the Schrödinger Equation, MATCH Commun. Math. Comput. Chem., 60, 3, 753771 (2008).
P8. Z.A. Anastassi and T.E. Simos: New Trigonometrically Fitted SixStep Symmetric Methods for the Efficient Solution of the Schrödinger Equation, MATCH Commun. Math. Comput. Chem., 60, 3, 733752 (2008).
P7. Z.A. Anastassi and T.E. Simos: A Family of ExponentiallyFitted RungeKutta Methods with Exponential Order up to Three for the Numerical Solution of the Schrödinger Equation, Journal of Mathematical Chemistry, 41, 1, 79100 (2007).
P6. Z.A. Anastassi and T.E. Simos: A TrigonometricallyFitted RungeKutta Method for the Numerical Solution of Orbital Problems, New Astronomy, 10, 301309 (2005).
P5. Z.A. Anastassi and T.E. Simos: Trigonometrically Fitted Fifth Order RungeKutta Methods for the Numerical Solution of the Schrödinger Equation, Mathematical and Computer Modelling, 42 (78), 877886 (2005).
P4. Z.A. Anastassi and T.E. Simos: Trigonometrically Fitted RungeKutta Methods for the Numerical Solution of the Schrödinger Equation, Journal of Mathematical Chemistry, 37, 3, 281293 (2005).
P3. Z.A. Anastassi and T.E. Simos: A DispersiveFitted and DissipativeFitted Explicit RungeKutta method for the Numerical Solution of Orbital Problems, New Astronomy, 10, 3137 (2004).
P2. Z.A. Anastassi and T.E. Simos: An Optimized RungeKutta method for the Solution of Orbital Problems, Journal of Computational and Applied Mathematics, 175, 19 (2005).
P1. Z.A. Anastassi and T.E. Simos: Special Optimized RungeKutta methods for IVPs with Oscillating Solutions, International Journal of Modern Physics C, 15, 115 (2004).
Abstracts in Conference Proceedings
C36. S. ColreavyDonnelly, S. Kuhn, F. Caraffini, S. O'Connor, Z. Anastassi, S. Coupland, A Neural Network for Interpolating LightSources, 4th IEEE International Workshop on Software Engineering for Smart Systems  IEEE Computer Society Signature Conference on Computers, Software and Applications (COMPSAC), Madrid, Spain, July 2020.
C35. J. Bielby, S. Kuhn, S. ColreavyDonnelly, F. Caraffini, S. O'Connor, Z.A. Anastassi, Identifying Parkinson's Disease Through the Classification of Audio Recording Data, IEEE World Congress on Computational Intelligence (IEEE WCCI), Glasgow, UK, July 2020.
C34. Z.A. Anastassi, G. Fotopoulos, D.J. Frantzeskakis, T.P. Horikis, N.I. Karachalios, P.G. Kevrekidis, I.G. Stratis, and K. Vetas, Numerical simulations of a nonlinear Schrödinger model with gain and loss, The 27th Biennial Numerical Analysis Conference 2017 (NANCONF 2017).
C33. Z.A. Anastassi, Fitted Linear Multistep Methods for the Solution of Periodic Differential Equations, Computational Techniques and Applications Conference (CTAC 2016).
C32. F. Tsitoura, Z. A. Anastassi, J. L. Marzuola, P. G. Kevrekidis, and D. J. Frantzeskakis, Computation of Dark Solitons near Potential and Nonlinearity Steps, Global Conference on Applied Physics & Mathematics 2016.
C31. Z.A. Anastassi, A.A. Kosti, A family of optimized symmetric linear multistep methods for the numerical solution of differential equations, 3rd ECCOMAS Young Investigators Conference (YIC 2015).
C30. Z.A. Anastassi, A.A. Kosti, A new RungeKuttaNyström pair for the numerical solution of periodic initial value problems, 14th International Conference Computational and Mathematical Methods in Science and Engineering, (CMMSE 2014).
C29. A.A. Kosti, Z.A. Anastassi, T.E. Simos, A Fitted RungeKuttaNyström Method with Fifth Order for the Integration of the TwoBody Problem, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2011, Conference Proceedings, 1389, 15971600, included in Thomson ISI Proceedings.
C28. Z.A. Anastassi, T.E. Simos, Some Symmetric Linear FourStep Methods for the Numerical Solution of Oscillatory Initial Value Problems, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2011, AIP Conference Proceedings, 1389, 16011604, included in Thomson ISI Proceedings.
C27. Z.A. Anastassi, Symposium on the Numerical Solution of Differential Equations and their Applications, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2011, AIP Conference Proceedings.
C26. G.A. Panopoulos, Z.A. Anastassi, T.E. Simos, Optimized Explicit Symmetric Linear Multistep Methods for the Numerical Solution of the Schrödinger Equation and Related Orbital Problems, Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2009), AIP Conference Proceedings, 1504, 13441347, included in Thomson ISI Proceedings.
C25. A.A. Kosti, Z.A. Anastassi, T.E. Simos, The development of an explicit RungeKuttaNyström method with infinite order of phaselag, dissipation error and the first derivative of dissipation error for the integration of the TwoBody Problem, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2010, AIP Conference Proceedings.
C24. A.A. Kosti, Z.A. Anastassi, T.E. Simos, The integration of the TwoBody Problem by using a new optimized explicit RungeKuttaNyström method with infinite order of phaselag, amplification factor and the first derivative of the phaselag, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2010, AIP Conference Proceedings.
C23. A.A. Kosti, Z.A. Anastassi, T.E. Simos, Construction of an optimized Runge Kutta method with increased phaselag order for the numerical solution of the Schrödinger equation, Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2009), AIP Conference Proceedings, 1504, 11821184 (2012) included in Thomson ISI Proceedings.
C22. A.A. Kosti, Z.A. Anastassi, T.E. Simos, Construction of an explicit RungeKuttaNyström method with constant coefficients and of a phasefitted and amplificationfitted explicit RungeKutta Nyström method for the numerical solution of the Schrödinger equation, Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2009), AIP Conference Proceedings, 1504, 11851187, included in Thomson ISI Proceedings.
C21. A.A. Anastassi, Z.A. Anastassi and T.E. Simos, Analysis of a RungeKutta Method Developed with Artificial Neural Networks, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2010, AIP Conference Proceedings.
C20. N.G. Tselios, Z.A. Anastassi and T.E. Simos, Optimized ThreeStage Implicit RungeKutta Methods for the Numerical Solution of Problems with Oscillatory Solutions, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2010, AIP Conference Proceedings, 1281, 22522255 (2010), included in Thomson ISI Proceedings.
C19. N.G. Tselios, Z.A. Anastassi and T.E. Simos, Optimized TwoStage Implicit RungeKutta Methods for the Numerical Solution of Problems with Oscillatory Solutions, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2010, AIP Conference Proceedings, 1281, 22482251 (2010), included in Thomson ISI Proceedings.
C18. Z.A. Anastassi and T.E. Simos, A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schrödinger Equation and Related Problems, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2010, AIP Conference Proceedings, 1281, 18431845 (2010), included in Thomson ISI Proceedings.
C17. D.F. Papadopoulos, Z.A. Anastassi and T.E. Simos, The Use of PhaseLag and Amplification Error Integrators for the Numerical Solution of the Radial Schrödinger Equation, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2010, AIP Conference Proceedings, 1281, 18391842 (2010), included in Thomson ISI Proceedings.
C16. Z.A. Anastassi, Symposium on the Numerical Solution of Differential Equations and their Applications, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2010, AIP Conference Proceedings, 1281, 18201820 (2010), included in Thomson ISI Proceedings.
C15. Z.A. Anastassi and T.E. Simos, Linear Multistep Methods for the Efficient Integration of the Schrödinger Equation, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2009, AIP Conference Proceedings, 1168, 16081611 (2009), included in Thomson ISI Proceedings.
C14. D.F. Papadopoulos, Z.A. Anastassi and T.E. Simos, A Zero Dispersion RKN Method for the Numerical Integration of Initial Value Problems with Oscillating Solutions, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2009, AIP Conference Proceedings, 1168, 550553, (2009), included in Thomson ISI Proceedings.
C13. D.F. Papadopoulos, Z.A. Anastassi and T.E. Simos, A Modified Zero Dispersion and Zero Dissipation RKN Method for the Numerical Solution of the Radial Schrödinger Equation, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2009, AIP Conference Proceedings, 1168, 16041607 (2009), included in Thomson ISI Proceedings.
C12. D.F. Papadopoulos, Z.A. Anastassi and T.E. Simos, The Use of PhaseLag and Amplification Error Derivatives in the Numerical Integration of ODEs with Oscillating Solutions, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2009, AIP Conference Proceedings, 1168, 547549 (2009), included in Thomson ISI Proceedings.
C11. Z.A. Anastassi, Symposium on the Numerical Solution of Differential Equations and their Applications, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2009, AIP Conference Proceedings, 1168, 15811581 (2009).
C10. Z.A. Anastassi, D.S. Vlachos and T.E. Simos, The Use of PhaseLag Derivatives in the Numerical Integration of ODEs with Oscillating Solutions, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2008, AIP Conference Proceedings, 1048, 10201025 (2008), included in Thomson ISI Proceedings.
C9. Z.A. Anastassi, Symposium on the Numerical Solution of Differential Equations and their Applications, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2008, AIP Conference Proceedings, 1048, 10011001 (2008).
C8. Z.A. Anastassi and T.E. Simos: A Family of Numerical Methods for the Efficient Solution of the Schrödinger Equation and Related Problems, Meeting “Gene around the World”.
C7. Z.A. Anastassi, D.S. Vlachos and T.E. Simos: Construction of General Linear Methods with Parallel Stages, Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE) 2006, 132136, VSP Brill, included in Thomson ISI Proceedings.
C6. Z.A. Anastassi and T.E. Simos: A TrigonometricallyFitted PStable Multistep Method for the Numerical Integration of the NBody Problem, Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE) 2006, 455457, VSP Brill, included in Thomson ISI Proceedings.
C5. Z.A. Anastassi and T.E. Simos: A DispersiveFitted and DissipativeFitted RungeKutta Method for IVPs with Oscillating Solutions, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2005, 866868, WileyVC.
C4. Z.A. Anastassi and T.E. Simos: A Trigonometrically Fitted RungeKutta Pair of Orders Four and Five for the Numerical Solution of the Schrödinger Equation, Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE) 2004, VSP Brill, 535538.
C3. Z.A. Anastassi and T.E. Simos: Trigonometrically Fitted RungeKutta Methods of Order Five for the Numerical Solution of the Schrödinger Equation, Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE) 2004, 3336, VSP Brill.
C2. Z.A. Anastassi and T.E. Simos: TrigonometricallyFitted RungeKutta Methods for the Numerical Solution of the Schrödinger Equation, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2004, WileyVCH, 2123, included in Thomson ISI Proceedings.
C1. Z.A. Anastassi and T.E. Simos: A family of Optimized RungeKutta methods with five stages and fourth order for IVPs with Oscillating Solutions, Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE) 2003, World Scientific, 2223.