Publications of Ch. Tsitouras

    Edited Volumes

  1. T. E. Simos and Ch. Tsitouras (editors), "International Conference in Numerical Analysis and Applied Mathematics (ICNAAM 2004)", Wiley-VCH, 2004.
  2. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2005, Wiley-VCH, 2005.
  3. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2006, Wiley-VCH, 2006.
  4. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2007, AIP CP 936, ISBN 978-0-7354-0447-2.
  5. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2008, AIP CP 1048, ISBN: 978-0-7354-0576-9.
  6. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2009, AIP CP 1168, ISBN: 978-0-7354-0705-3.
  7. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2010, AIP CP 1281, ISBN: 978-0-7354-0834-3.
  8. T. E. Simos, G. Psihoyios , Ch. Tsitouras and Z. Anastassi (editors), ICNAAM 2011, AIP Conf. Proc. 1389, ISBN: 978-0-7354-0956-9.
  9. T. E. Simos, G. Psihoyios , Ch. Tsitouras and Z. Anastassi (editors), ICNAAM 2012, AIP Conf. Proc. 1479, ISBN: 978-0-7354-1091-6.
  10. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2013, AIP Conf. Proc. 1558, ISBN: 978-0-7354-1184-5.
  11. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2014, AIP Conf. Proc. 1648, ISBN: 978-0-7354-1287-3.
  12. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2015, AIP Conf. Proc.1738, ISBN: 978-0-7354-1392-4
  13. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2016, AIP Conf. Proc.1863, ISBN: 978-0-7354-1538-6

Publications in refereed journals

  1. G.Papageorgiou and Ch.Tsitouras, "Scaled Runge-Kutta-Nystrom methods for the second order differential equation y''=f(x,y)", Int. J. Comput. Math. 28(1988), 139-150.
  2. G. Papageorgiou, Th. Simos and Ch. Tsitouras, "Some new Runge-Kutta methods with interpolation properties and their application to the magnetic binary problem", Celestial Mechanics 44(1988), 167-177.
  3. Ch. Tsitouras and G. Papageorgiou, "New interpolants for Runge-Kutta algorithms using second derivatives", Int. J. Comput. Math. 31(1989) 105-113.
  4. Ch. Tsitouras and G. Papageorgiou, "Runge-Kutta interpolants based on values from two successive integration steps", Computing 43(1990), 255-266.
  5. Ch. Tsitouras, G. Papageorgiou and T. Kalvouridis, "Efficiency of Runge-Kutta-Nystrom methods in solving problems of Celestial Mechanics of the form y"=f(x,y,y')", Celestial Mechanics 53(1992), 329-346.
  6. Ch. Tsitouras and G. Papageorgiou, "Interpolating Runge-Kutta-Nystrom methods of High order", Int. J. Comput. Math. 47(1992), 209-217.
  7. G. Papageorgiou, Ch. Tsitouras and S. N. Papakostas, "Runge-Kutta pairs for periodic initial value problems", Computing 51(1993), 151-163.
  8. S. N. Papakostas, Ch Tsitouras and G. Papageorgiou "A new family of efficient 6(5) Runge-Kutta pairs", SIAM J. Numerical Analysis 33(1996), 917-936.
  9. G. Papageorgiou and Ch. Tsitouras, "Continuous Runge-Kutta(-Nystrom) methods with reduced Phase-errors", J. Comput. Appl. Math. 69(1996), 1-11.
  10. G. Papageorgiou and Ch. Tsitouras, "Interpolation for high order Runge-Kutta methods", Int. J. Comput. Math. 65(1997) 273-291.
  11. S. N. Papakostas and Ch.Tsitouras, "Highly Continuous Interpolants for One-Step ODE Solvers and their Application to Runge-Kutta Methods", SIAM J. Num. Anal. 34(1997), 22-47.
  12. Th. Simos and Ch. Tsitouras,"A P-stable eighth order method for the numerical integration of periodic initial value problems", J. Comput. Phys., 130(1997), 123-128.
  13. Ch. Tsitouras and Th. Simos, "High order explicit methods for the integration of periodic initial value problems" Appl. Math. & Comput. 95(1998), 15-26.
  14. Ch. Tsitouras "A parameter study of explicit Runge-Kutta pairs of orders 6(5)", Appl. Math. Letters 11(1998) 65-69.
  15. G. Papageorgiou, I. Famelis and Ch. Tsitouras "A P-stable Diagonally Implicit Runge-Kutta-Nystrom method", Numerical Algorithms 17(1998) 345-353.
  16. Ch. Tsitouras, "High order zero-dissipative Runge-Kutta-Nystrom methods", J. Comput. Appl. Math. 95(1998) 157-161.
  17. Ch. Tsitouras, "High algebraic order, high dissipation order Runge-Kutta methods", Comput. & Math. w Appl. vol37 i6(1999) 31-36.
  18. Ch. Tsitouras and S. N. Papakostas, "Cheap Error Estimation for Runge-Kutta methods", SIAM J. Sci. Comput. 20(1999) 2067-2088. (postscript version 439K)
  19. Ch. Tsitouras, "A tenth order symplectic Runge-Kutta-Nystrom method", Celestial Mechanics & Dynamical Astronomy 74(1999) 223-230. (postscript version 93K)
  20. S. N. Papakostas and Ch. Tsitouras, "High Phase-Lag Order Runge-Kutta and Nystrom Pairs", SIAM J. Sci. Comput. 21(2000) 747-763. (postscript version 407K)
  21. Ch. Tsitouras, "Dissipative high phase-lag order methods", Appl. Math. & Comput. 117(2001) 35-43. (postscript version 100K)
  22. Ch. Tsitouras, "Explicit Numerov type methods with reduced number of stages", Comput. & Math. w Appl., 45(2003) 37-42. (postscript version 79K)
  23. Ch. Tsitouras, "Optimized explicit Runge-Kutta pair of orders 9(8)", Appl. Numer. Math., 38(2001) 123-134. (postscript version 134K)
  24. Ch. Tsitouras and Th. Simos, "High order imbedded Numerov-Type methods for the solution of periodic problems", Appl. Math. & Comput., 131(2002) 201-211.
  25. G. Papageorgiou, Ch. Tsitouras and I. Famelis, "Explicit Numerov type methods for second order IVPs with oscillating solutions", Int. J. Mod. Phys. C 12(2001) 657-666. (postscript version 118K)
  26. Ch. Tsitouras, "Explicit Runge-Kutta pairs appropriate for engineering applications", Appl. Math. Model., 26(2002) 77-88.
  27. Ch. Tsitouras, "Runge-Kutta methods for the numerical solution of Initial Value problems", Cubo Matematica Educacional , vol 4, no 2 (2002) 183-199.
  28. Ch. Tsitouras, "Families of Numerov type methods with high phase-lag order", Appl. Math. & Comput., 135(2003) 169-178.
  29. Ch. Tsitouras, "Explicit two step methods for second order linear IVPs", Comput. Math. Appl., 43(2002) 943-949. (pdf version 504K)
  30. Ch. Tsitouras, "Neural Networks with multi dimensional transfer functions", IEEE T Neural Networks, 13 (2002) 222-228.(pdf version 181K)
  31. G. Papageorgiou and Ch. Tsitouras, "Runge-Kutta pairs for scalar autonomous IVPs", Int. J. Comput. Math., 80(2002) 201-209.(pdf version 106K)
  32. Ch. Tsitouras and Th. Simos, "Optimized RK pairs for problems with oscillating solutions" J. Comput. Appl. Math. 147(2002) 397-409.(postscript version 142K)
  33. I. Famelis S. N. Papakostas and Ch. Tsitouras, "Symbolic derivation of Runge-Kutta order conditions" , J. Symbol. Comput. 37(2004) 311-327. (pdf version 167K)
  34. Th. Simos, I. Famelis and Ch. Tsitouras, "Zero dissipative, explicit Numerov type methods for second order IVPs with oscillating solutions" , Numerical Algorithms 34(2003) 27-40.
  35. Psarrakos, P. and Tsitouras Ch., "Numerical Approximation of the boundary of the Numerical Range of Matrix Polynomials", Appl. Numer. Anal. & Comput. Math., 2(2005) 126-133. (pdf version 384K)
  36. A. G. Bratsos, Ch. Tsitouras and D. G. Natsis, "Linearized numerical schemes for the Boussinesq equation", Appl. Numer. Anal. & Comput. Math., 2(2005) 34-53.
  37. D. G. Pavlou, N. V. Vlachakis, Ch. Tsitouras, M. G. Pavlou and A. Fatsis, "Creep sagging analysis of pressure pipes", Comput. Mater. Sci., 36(2006) 303-309.
  38. Ch. Tsitouras, "Stage Reduction on P-Stable Numerov Type Methods of Eighth Order", J. Comput. Appl. Math., 191(2006) 297-305.( pdf version 110K)
  39. A. G. Bratsos, I. Th. Famelis, A. Kollias and Ch. Tsitouras, "Phase-Fitted Numerov type methods", Appl. Math. & Comput., 2 (2005) 34-53.
  40. Ch. Tsitouras, "Explicit eighth order two-step methods with nine stages for integrating oscillatory problems", Int. J. Modern Phys. C, 17(2006) 861-876. (pdf version 384K)
  41. Ch. Tsitouras and I. Th. Famelis, "Symbolic derivation of Runge-Kutta-Nystrom order conditions", J. Math. Chem., 46 (2009) 896-912, (pdf version 199K).
  42. Ch. Tsitouras and I. Th. Famelis, "Quadratic SDIRK for chemical reaction problems", MATCH-Commun. Comput. Math. Chem., 60 (2008) 697-710. (pdf version 168K).
  43. G.Pavlou, I. Mavrothanasis, Ch. Tsitouras, S. Avlonitis, V. N. Vlachakis, and M.G. Pavlou, "Stress Concentration Analysis of Interfacial Micro-structural Cracks under Internal Singular Loading Sources", J. Comput. Meth. Sci. Engnr., 10 (2010) 3-12.
  44. Ch. Tsitouras, "Runge-Kutta interpolants for high precision computations", Numer. Algorithms, 44 (2007) 291-307. (pdf version 200K, coefficients)
  45. I. Th. Famelis and Ch. Tsitouras "Symbolic Derivation of Order Conditions for Hybrid Numerov-type methods solving y''=f(x,y)", J. Comput. Appl. Math., 218 (2008) 543-555. (pdf version 199K).
  46. Ch. Tsitouras and I. Th. Famelis, "Quadratic Stormer-type methods for the solution of the Boussinesq equation by the method of lines", Numer. Meth. PDEs, 24 (2008) 1321-1328.(pdf version 173K).
  47. Ch. Tsitouras,  "Rational Approximations to the Solution of the Brusselator System Compared to the Adomian Decomposition Method", Int. J. Contemp. Math. Sci., 4 (2009) 815-820. pdf version
  48. Ch. Massouros and Ch. Tsitouras, "Enumeration of hypercompositional structures defined by binary relations", Italian J. Pure & Appl. Maths., 28 (2011) 43-54.(pdf version 109K ).
  49. Ch. Tsitouras and Ch. Massouros, "On Enumeration of Hypergroups of Order 3", Comput. Maths. Appl., 59 (2010) 519-523. (pdf version 151K )
  50. Ch. Tsitouras, "Rational Approximation to the Abelian Differential Equation Compared to the Abelian Method", Int. J. Comput. Math. & Numer. Simul.., 4 (2011) 45-49.
  51. Ch. Tsitouras, "Greatest Remainder Bi-proportional Rounding and the Greek Parliamentary Elections of 2007", Appl. Math. Comput., 217 (2011) 9254-9260. (pdf version 130K)
  52. Ch. Tsitouras, "Runge-Kutta pairs of orders 5(4) satisfying only the first column simplifying assumption", Comput. Maths. Appl., 62 (2011) 770-775. (pdf version 139K), (Mathematica code)
  53. Ch. Tsitouras, I. Th. Famelis and T. E. Simos, "On modified RK trees and methods", Comput. Maths. Appl., 62 (2011) 2101-2111. (pdf version 236K )
  54. Ch. Tsitouras, "Hybrid Hamilton-Webster and the Greek apportionment", Appl. Math. Comput., 218 (2011) 3957-3961. (pdf version 108K, Matlab Implementation)
  55. Ch. Tsitouras and I. Th. Famelis, "Using Neural Networks for the derivation of Runge-Kutta-Nystrom pairs for integration of orbits", New Astronomy, 17 (2012) 469-473. (pdf version 135K)
  56. Ch. Tsitouras and C. G. Massouros, "Enumeration of Rosenberg type Hypercompositional structures defined by binary relations", Eur. J. Combin., 33 (2012) 1777-1786. (pdf version 179K)
  57. Ch. Tsitouras, "On fitted modifications of Runge--Kutta--Nystrom Pairs", Appl. Math. Comput., 232 (2014) 416-423. (pdf version 94K)
  58. Ch. Tsitouras and V. N. Katsikis, "Bounds for Variable Degree Rational Loo Approximations to the Matrix Cosine", Comput. Phys. Commun., 185 (2014) 2834-2840.(pdf version 135K)
  59. I. Th. Famelis and Ch. Tsitouras, "Quadratic Shooting Solution for a Environmental Parameter Prediction Problem", Far East J. of Appl. Math., 91 (2015), 81.
  60. I. Th. Famelis and Ch. Tsitouras, "On modifications of Runge-Kutta-Nystrom methods for solving y''''=f(x,y)", Appl. Math. Comput., 273 (2016) 726-734.
  61. Ch. Tsitouras, T. E. Simos and I. Th. Famelis, "Phase-fitted Runge-Kutta pairs of orders 8(7)", J. Comput. Appl. Math., 321 (2017) 226-231.
  62. I. Th. Famelis and Ch. Tsitouras, "Symbolic derivation of Runge-Kutta-Nyström type order conditions and methods for solving y''' = f (x, y )", Appl. Math. Comput., 297 (2017) 50-60.
  63. T. E. Simos and Ch. Tsitouras, "Evolutionary Generation of High Order Explicit Two Step Methods for Second Order Linear IVPs.", Math. Meths Appl. Sci., (2017) 1-9. https://doi.org/10.1002/mma.4454.
  64. T. E. Simos, Ch. Tsitouras and I. Th. Famelis, "Explicit Numerov type methods with constand coefficients: A Review", Appl. Comput. Math., 16 (2017) 89-113.
  65. I. Th. Famelis, A. Alexandridis, Ch. Tsitouras, "High Accuracy Hybrid DE-PSO Algorithm for the construction of Runge Kutta pairs", Enginr. Optim., to appear.
  66. T. E. Simos and Ch. Tsitouras, "A new family of seven stages, eighth order explicit Numerov-type methods", Math. Meths Appl. Sci., to appear.
  67. D. B. Berg, T. E. Simos and Ch. Tsitouras, "Trigonometric fitted, eighth order explicit Numerov-type methods", Math. Meths Appl. Sci., to appear.

    Submitted for publication

    1. T. E. Simos and Ch. Tsitouras, "On ninth order, explicit Numerov type methods with constant coefficients".

    Conference Proceedings

    1. G. Papageorgiou, T. Kalvouridis and Ch. Tsitouras, "Scaled Runge-Kutta methods: The powerful algorithms for the approximate solution of Dynamical problems", 2nd National Congress on Mechanics, Athens, June 29-July 1, 1989. pp99-108.
    2. R. Krikkis, Ch. Tsitouras and G. Kakatsios, "Generalized steady one dimensional flow for real cases", Amer.Soc. Mech. Engin., Conference Proceedings (1991), 1011-1024.
    3. G. Papageorgiou, Ch. Tsitouras and S. N. Papakostas, "5-th and 6-th order Runge-Kutta pairs for initial value problems with periodical solutions", ERMIS conference, Athens 1992, pp487-497.
    4. S. N. Papakostas, Ch. Tsitouras and G. Papageorgiou, "A new family of efficient 6(5) Runge-Kutta pairs", ERMIS conference, Athens 1992, pp515-516.
    5. M. Lambiris, Ch. Tsitouras and K. Evmorfopoulos, "Four-step, Two-stage, Sixth-order P-Stable methods", Proceedings of ICCMSE 2003, World Scientific, pp337-339 (pdf version 77K).
    6. G. Papageorgiou and Ch. Tsitouras, "Runge-Kutta research at NTUA", Proceedings of ICCMSE 2003, World Scientific, pp xx-xx (pdf version 35K).
    7. D. G. Pavlou, Ch. Tsitouras, N. V. Vlachakis, M. G. Pavlou and V. N. Vlachakis, "Non Linear Stress Analysis of Pressure Pipes under Creep conditions", Proceeidings of ICNAAM 2004, Wiley-VCH, pp 307-311.
    8. Psarrakos, P. and Tsitouras Ch., "Numerical Approximation of the boundary of the Numerical Range of Matrix Polynomials", Proceeidings of ICNAAM 2004, Wiley-VCH, pp 318-320.
    9. P. I. Arsenos, C. Demakos, Ch. Tsitouras, D. G. Pavlou and M. G. Pavlou, "Derivation and Optimization of the Material Cost Function for Natural Gas Pipe- Lines", Lecture Series on Computer and Computational Sciences, VSP, pp 41-44.
    10. A. G. Bratsos, I. Th. Famelis and Ch. Tsitouras, "Phase-Fitted Numerov type methods", Lecture Series on Computer and Computational Sciences, VSP, pp 87-90.
    11. Ch. Tsitouras, "Stage Reduction on P-Stable Numerov Type Methods of Eighth Order", Lecture Series on Computer and Computational Sciences, VSP, pp 510-513.
    12. Ch. Tsitouras and I. Th. Famelis, "Quadrature Numerov-type methods for the solution of Boussinesq equation by the method of lines", 17th World IMACS Congress, Paris 2005, paper T2-I-21-0170. (pdf version)
    13. A. G. Bratsos, Ch. Tsitouras and D. G. Natsis, "An extrapolated linearized finite-difference scheme for the numerical solution of the Boussinesq equation", 17th World IMACS Congress, Paris 2005, paper T2-I-21-0170. (pdf version)
    14. Ch. Tsitouras, Ch. Masouros and M. Lambiris, A Mathematica package enumerating Hypergroups of order 3, Proceeidings of ICNAAM 2005, Wiley-VCH
    15. Ch. Tsitouras and I. Th. Famelis, "Phase-Fitted modified Runge-Kutta pairs of orders 6(5)", ICNAAM 2006, Crete, 2006 (pdf version 105K).
    16. Y. G. Petalas, Ch. Tsitouras, G. S. Androulakis and M. N. Vrahatis, "Evolutionary generation of Runge--Kutta pairs", Proceeidings of ICNAAM 2006, pp 433-437 (pdf version 120K)..
    17. V. Katsikis and Ch. Tsitouras, "Computational methods in finite differential lattice subspaces: An application in economics", Proceeidings of ICNAAM 2006, pp 406-410.
    18. Y. G. Petalas, Ch. Tsitouras, G. S. Androulakis and M. N. Vrahatis, "Generating Symmetric Composition Methods through Memetic Algorithms", Lecture Series on Computer and Computational Sciences, VSP 2006 (pdf version 149K).
    19. A. Fatsis, Ch. Tsitouras, A. Panoutsopoulou and N. Vlachakis, "Mathematical Formulation of 3D Non-Reflecting Boundary Conditions for Hyperbolic Equations for Internal Flows in Thermal Engines", AIP CP936 (2007) 199-203.
    20. Ch. Tsitouras, "Greek Electoral System: Optimal Distribution of the Seats", AIP CP936 (2007) 555-557.
    21. Ch. Tsitouras, "Using Neural Networks for the Derivation of Runge-Kutta-Nystrom Pairs", AIP CP1048 (2008) 1034-1036. (pdf version 35K)
    22. Ch. Massouros, Ch. Tsitouras and S. Voliotis, "Square Roots of Total Boolean Matrices", ICSSIP 2009, doi:10.1109/IWSSIP.2009.5367718 (pdf version 220K)
    23. Ch. Tsitouras, "Runge-Kutta pairs of orders 5(4) using the minimal set of simplifying assumptions", AIP CP1168 (2009) 69-72. (pdf version 39K)
    24. version 220K)
    25. Ch. Tsitouras, "Trigonometric fitted Runge-Kutta-Nystrom pair of orders 6(4)", AIP CP1558 (2013) 2509-2511.
    26. I. Th. Famelis and Ch. Tsitouras, "Quadratic RK Shooting solution for a Environmental Parameter Prediction Boundary Value Problem", AIP CP 1618 (2014) 839-842.
    27. Ch. Tsitouras and V. N. Katsikis, "Solving undamped unforced free oscillators by Loo approximations to cos", AIP CP 1618 (2014) 824-827.
    28. Ch. Tsitouras, "Evolutionary derivation of quadratic symplectic Runge-Kutta-Nystrom methods", AIP CP 1648 (2015) No740002.
    29. A. Alexandridis, I. Th. Famelis and Ch. Tsitouras, "Long-term time-series prediction using radial basis function neural networks", AIP CP 1648 (2015) No740003.
    30. I. Th. Famelis and Ch. Tsitouras, "Differential evolution for the derivation of Runge Kutta pairs", AIP CP 1648 (2015) No740004.
    31. I. Th. Famelis and Ch. Tsitouras, "On the modification of Differential Evolution strategy for the construction of Runge Kutta pairs", MCEEA’15, MATEC Web of Conferences, Volume 41 (2016), https://doi.org/10.1051/matecconf/20164105001.
    32. I. Th. Famelis, S. Tsitmidelis and Ch. Tsitouras, "On the modification of Differential Evolution strategy for the construction of Runge Kutta pairs", MCEEA’15, MATEC Web of Conferences, Volume 41 (2016), https://doi.org/10.1051/matecconf/20164105002.
    33. S. N. Papakostas, S. Tsitmidelis and C Tsitouras, "Evolutionary Generation of 7th order Runge - Kutta - Nyström Type Methods for Solving y'''' =f(x,y)", AIP CP 1702 (2016) No 190018.
    34. Ch. Tsitouras and I. Th. Famelis, "Minimax vs Pade Approximation of Matrix Exponential for Normal and Nonnegative Matrices", AIP CP 1702 (2016) No 190013.
    35. V. N. Katsikis, S. N. Papakostas, S. Tsitmidelis and Ch Tsitouras, "Evolutionary generation of explicit two step methods for second order linear IVPs", AIP CP 1738 (2016) No 480038.
    36. I. Th. Famelis, S. Tsitmidelis and Ch. Tsitouras, "Evolutionary Generation of high oder Runge - Kutta - Nyström type pairs for solving y''''=f(x,y)",AIP CP 1738 (2016) No 480037.
    37. A. Alexandridis, I. Th. Famelis and Ch. Tsitouras, "Particle Swarm Optimization for Complex Nonlinear Optimization Problems", AIP CP 1738 (2016) No480120.
    38. I. Th. Famelis and Ch. Tsitouras, "High Phase-Lag Order Runge Kutta Pairs of Orders 8(7)", AIP CP 1863 (2017) No560031.

    Other work

    1. G.Papageorgiou and Ch.Tsitouras, "Practical Runge-Kutta-Nystrom methods for the equation y''=f(x,y), with interpolation properties", Dept. of Math.,Tech. Rep #1/1987,42pg., NTUA.
    2. Ch. Tsitouras ''Methods for dense output in Runge-Kutta algorithms'', M.Sc. Dissertation, in Greek, University of Athens, 1988.
    3. Ch. Tsitouras ''Continuous extensions of Runge-Kutta type methods for Initial value problems'', Ph.D. dissertation, in Greek, Athens 1990.
    4. G. Papageorgiou and Ch. Tsitouras, "High order Runge-Kutta & Runge-Kutta-Nystrom interpolants", Conference on the Solution of ODE's, Helsinki, June 1990.
    5. G. Papageorgiou and Ch. Tsitouras, "Runge-Kutta-Nystrom interpolants with reduced phase Errors", 1st Numerical Analysis Conference, Plovdiv Bulgaria, August 1992.
    6. G. Papageorgiou, Ch. Tsitouras and S. N. Papakostas, "Runge-Kutta pairs for periodic initial value problems", NTUA, Dept. of Math., Tech. Rep. NA 93-1.
    7. Z. Kalogiratou and Ch. Tsitouras, "Intermediate reconsideration of Runge-Kutta step" conference on Scientific Computing and Differential Equations, Grado 1997, B. Owren editor. (postscript version 97K)
    8. Ch. Tsitouras and I. Th. Famelis, "Study and development of Nystrom - type methos for integration of Hamiltonian problems", CHAOS 2013, 11-14 June 2013, Istanbul, Turkey.
    9. Ch. Tsitouras, V. N. Katsikis and I. Th. Famelis, "Rational Loo approximations to the matrix cosine", SCICADE 2013, September 16-20, 2013, Valladolid, Spain.

    Published software

    1. Matlab file ode86 for integration of system of ODEs (Journal Paper No18).
    2. Matlab file rkn86 for integration of system of ODEs of second order (Journal Paper No20).
    3. Mathematica file trees16n.m for derivation Runge-Kutta order conditions (Journal Paper No33).
    4. Mathematica file rkn-symbolic.m for symbolic derivation of Runge-Kutta-Nystrom order conditions (Journal Paper No41).
    5. Mathematica file NumericalAlgorithms.txt for the coefficients of the RK9(8) pair and interpolants (Journal Papers No23 & 44).
    6. Mathematica file and Notebook NumerovSymbCode.zip for two-step Numerov Type methods. (Journal Paper No45).
    7. Mathematica file HyperGroupTest.m for checking HyperGroups (Journal Paper No49).
    8. Mathematica file new54.m producing RK5(4) family pairs (Journal Paper No52).

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