Stepan Shakhno

Position: Chairperson, Theory of Optimal Processes Department

Scientific degree: Doctor of Physical and Mathematical Sciences

Academic status: Professor

Phone (office): (032) 239-43-91

Email: stepan.shakhno@lnu.edu.ua

Web page: ami.lnu.edu.ua

Google Scholar profile: scholar.google.com.ua

Research interests

Numerical methods for solving of nonlinear functional equations, nonlinear boundary value problems, iterative methods for solving optimization problems and nonlinear least squares problems.

Courses

Selected publications

Selected Scientific Publication

  1. Shakhno S.M. , Iakymchuk R.  P., Yarmola H.P.  An iterative method for solving nonlinear least squares problems with nondifferentiable operator //  Matematychni Studii. – 2017. – Т.48, №1. – 97–107.
  2. Shakhno S. , Shunkin Yu.   One combined method for solving nonlinear least squares problems // Visnyk Lviv. Univ. Ser. Appl. math. inform. Issue  25, 2017.- P. 38-48 (Ukrainian).
  3. Shakhno S. , Yarmola H.   On convergence of Newto -Potra methodunder weak conditions // Visnyk Lviv. Univ. Ser. Appl. math. inform. Issue 25, 2017.- P. 49-55 (Ukrainian).
  4. Prokopyshyn I., Shakhno S. Differential-difference iterative domain decomposition algorithms for unilateral multibody contact problems of elasticity// Physico-mathematical modelling and informational technologies. –  2017, Issue  25.– P.  125-140 (Ukrainian).
  5. Iakymchuk R.P., Shakhno S.M., Yarmola H.P. Convergence analysis of a two-step modification of the Gauss-Newton method and its Applications // Journal of Computational and Applied Mathematics. – 2017. – № 3 (126).  – P.61- 74.
  6. Iakymchuk R., Shakhno S., Yarmola H. Combined Newton-Kurchatov method for solving nonlinear operator equations // PAMM · Proc. Appl. Math. Mech. 16(1):719-720 · October 2016, DOI: 10.1002/pamm.201610348.
  7. Shakhno S.M. , Shunkin Yu.V.   Two-step secant-type method for solving nonlinear equations // Journal of Computational and Applied Mathematics. – 2017. – №1 (124) (Ukrainian).
  8. Iakymchuk R., Shakhno S. Methods with Successive and Parallel Approximations of Inverse Operator for the Nonlinear Least Squares Problem // PAMM – Appl. Math. Mech., 15, 569-570 (2015) DOI 10.1002/pamm.201510274.
  9. Shakhno S. On the convergence of the accelerated Newton method under generalized Lipschitz conditions // Journal of Mathematical Sciences, January 2016, Volume 212,Issue 1, pp 16-26.
  10. Shakhno S.M., Babjak A.-V.I, Yarmola H.P. Combined  method Newton-Potra of the solution of nonlinear equations  // J. Numer. Appl. Math. . – 2015. – № 3 (120).  – P. 170-178. (Ukrainian).
  11. Shakhno S.M. Combined Newton-Kurchatov method under the generalized Lipschitz conditions for the derivatives and divided differences // J. Numer. Appl. Math. – 2015. – № 2 (119).  – P. 78-89 .
  12. Shakhno S.M. On the convergence of the accelerated Newton method under generalized Lipschitz conditions // Mathematical methods and physicomechanical fields. – 2014. – 57, № 1. – P. 16-34.(Ukrainian).
  13. Shakhno S.M. Yarmola H.P. About two-step Secant-like method for solving nonlinear equations // Matematychni studii. 2014.  V.42, №1. P.84–88.(Ukrainian).
  14. Shakhno S.M. Convergence of the two-step combined method and uniqueness of the solution of nonlinear operator equations// Journal of Computational and Applied Mathematics, 261 (2014) 378–38
  15. Shakhno S.M., Mel’nyk I.V., Yarmola H.P. Analysis of the convergence of a combined method for the solution of nonlinear equations // Journal of Mathematical Sciences, Vol. 201, No. 1, August, 2014. P.32-43.
  16. Shakhno S.M. Yarmola H.P. Two-step combined method for solving nonlinear operator equations // J. Numer. Appl. Math. – № 2 (116).  – P. 130-140.
  17. Iakymchuk R., Shakhno S. On the Local Convergence Analysis of a Two-Step Modification of the Gauss-Newton Method // PAMM · Proc. Appl. Math. Mech. 14, 813 – 814 (2014) / DOI 10.1002/pamm.201410387
  18. Shakhno S.M. Yarmola H.P.  Convergence conditions of the two-parametric secant type method for solving nonlinear equations taking into account errors // “Taurida Journal of Computer Science. Theory and Mathematics”, 2014, 2, 137-145.
  19. Shakhno S.M. Iterative-difference methods for for solving nonlinear operator equations // Comp. Appl. Math. 2012. – № 1 (107). P. 89-104 (Ukrainian).
  20. Shakhno S., Yarmola H. Two-step method for solving nonlinear equations with nondifferentiable operator // Numer. Appl. Math. 2012. – № 3 (109).  P. 105-115 .
  21. Shakhno S.M. Yarmola H.P.  Two-step method for solving nonlinear equations with nondifferentiable operator // Matematychni studii.  2011. Т 36, №2. С. 213-220 (Ukrainian).
  22. Shakhno S.M. Difference and parametric iterative methods for solving nonlinear problems, Thesis of dissertation of Doctor of Physics and Mathematics in speciality “Mathematical modeling and numerical methods” 2012. 35с. (Ukrainian).
  23. Shakhno S.M. Yarmola H.P. Application of twoparametric difference method for solving nonlinear integral // Lviv. Univ. Ser. Appl. Math Inform. – 2011. –№ 17. – P. 37-46(Ukrainian).
  24. Shakhno S.M. Yarmola H.P. Iterative-difference methods in the non-stationary problems of heat-conducting  // Comp. Modeling. Ser. Physics and Math. – 2010. – V. 3. – С.214-226(Ukrainian).
  25. Shakhno S.M. On a two-step iterative process under generalized Lipschitz conditions for first-order divided differences // Journal of Mathematical Sciences. – – V. 168,  No 4. – P. 576-584.
  26. Shakhno S.M. Convergence of inexact difference methods under the generalized Lipschitz conditions // Journal of Mathematical Sciences.  – – V. 171,  No 4. – P. 453-465.
  27. Шахно С.М. On a two-step iterative process under generalized Lipschitz conditions for first-order divided differences // Mathematical methods and physicomechanical fields. – 2009. – Т. 52. – № 1. – С. 59–66(Ukrainian).
  28. Shakhno S.M., Gnatyshyn O.P., Iakymchuk R.P. On a difference method with superquadratic сonvergence for solving nonlinear least squares problems // Lviv. univ. Ser. Appl. Math. Inform. V. 13. 2007. С. 51-58(Ukrainian).
  29. Shakhno S.M. Secant method under the generalized Lipschitz conditions for the divided difference operator // Visn. NTSH. V. 4. − 2007. − С. 296-305 (Ukrainian).
  30. Shakhno S.M. On the Secant method under the generalized Lipschitz conditions for the divided difference operator // PAMM. Vol.7, Issue 1, 2007, P 2060083- 2060084.
  31. Shakhno S.M. On the Steffensen method under the generalized Lipschitz conditions for the divided difference operator // PAMM. Vol.8, Issue 1, 2008, P 10855-10856.
  32. 14. Shakhno S.M. On an Iterative Algorithm with Superquadratic Convergence for Solving Nonlinear Operator Equations Journal of Computational and Applied Mathematics. Vol. 231 ,  Issue 1,   2009, pp. 222-235.
  33. Shakhno S.M. Steffensen method method under the generalized Lipschitz conditions for conditions for first-order divided differences // Matematychni studii. 2008. Т. 31. N 2. С. 90-95.
  34. Shakhno S.M., Iakymchuk R.P.  On a two-step modification of Gauss-Newton method  under the generalized Lipschitz conditions for nonlinear least squares problem // Visn. NTSH. V. 6. − 2009. − PP. 277–286 (Ukrainian).
  35. Shakhno S.M., Gnatyshyn O.P., Iakymchuk R.P. On a Secant Type Method for Nonlinear Least Squares Problems// J. Numer. Appl. 2009 № 1 (97) pp. 112-121.
  36. Shakhno S.M. Convergence of inexact difference methods under the generalized Lipschitz conditions // Meth. Phys.-Mech. Polia. 2009. V. 52. N 3. С. 30-40 (Ukrainian).
  37. Shakhno S.M., Grab S., Yarmola H.P. Twoparametric methods os secant type processes for solving nonlinear equations. // // Lviv. univ. Ser. Appl. Math. Inform. 2009. V. 11. С. 99-106 (Ukrainian).
  38. Shakhno S.M., Iakymchuk R.P. On one-step modification of Gauss-Newton method under generalized Lipschitz conditions for solving the nonlinear least squares problem //  PAMM. Vol. 9, Issue 1, 2009, P 565-566.
  39. Shakhno S.M. Numerical methods of linear algebra. – Lviv, 2007. 246 p. (Ukrainian).
  40. Shakhno S.M., Makukh O.M. Two- and three-step iterative processes for solving nonlinear equations. Visnyk Lviv. Univ. Ser. Appl. math. inform. 2006. V. 11. P. 99-106 (in Ukrainian).
  41. Shakhno S.M., Makukh O.M. About iterative methods in conditions of Holder continuity of the method divided differences of the second order. Mathematical methods and physicomechanical fields. 2006. Vol. 49. No 2. P. 90-98 (in Ukrainian).
  42. Shakhno S.M. On the difference method with quadratic convergence for solving nonlinear operator equations. Matematychni Studii. 2006. Vol. 26. No 1. P. 105-110 (in Ukrainian).
  43. Shakhno S.M., Gnatyshyn O.P. On an iterative algorithm of order 1.839. for solving the nonlinear least squares problems// Applied Mathematics and Computation. 2005. Vol. 161. P. 253-264.
  44. Shakhno S.M. Method of order 1+sqrt(2) for the solution of nonlinear equations with Hölder continuous divided differences. PAMM (Proc. Appl.Math.Mech.), Volume 5, Issue 1. 2005. 779-780.
  45. Shakhno S.M. Nonlinear majorants for investigation of methods of linear interpolation for the solution of nonlinear equations. European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004- P.Neittaanmäki, T.Rossi, K.Majava and O.Pironneau (eds.) O.Nevanlinna and R.Rannacher (assoc. eds.) Yuväskylä, 24-28 Jyli 2004, 11 p. http://www:mit.jyu.fi/eccomas2004/proceedings/pdf/424.pdf
  46. Shakhno S.M. On a Kurchatov’s method of linear interpolation for solving nonlinear equations. PAMM (Proc. Appl.Math.Mech.), Volume 4, Issue 1. 2004. 650-651.
  47. Shakhno S.M. Application of nonlinear majorants for investigation of Secant method for solving of nonlinear equations. Mathematical studios (Matematychni studii). v.22. N 1. 2004. p. 79-86 (in Ukrainian).
  48. Shakhno S.M., Gnatyshyn O.P. About some iterative-difference methods for solving of unconstrained minimization problems. Visnyk Lviv. Univ. Ser. prykl. matem. inform. 2003. Vyp. 6. P. 28-35 (in Ukrainian).
  49. Shakhno S.M., Makukh O.M. Local convergence of iterative-difference methods for solving nonlinear operator equations. Visnyk Lviv. Univ. Ser. prykl. matem. and inform. 2003. Vyp. 7. P. 124-131 (in Ukrainian).
  50. Dudykevych A.T., Levytska S.M., Shakhno S.M. Practical realization of methods of numerical integration. Methodical instructions. Publishing center Lviv Univ. 2002. 37 p.(in Ukrainian).
  51. Shakhno S.M. Investigation of Newton methods in which inner iterative processes are used. Journal of Mathematical Sciences. Vol. 109, N 1, March 2002, 1203-1208.
  52. Shakhno S.M., Gnatyshyn O.P. Application of Gauss-Newton-like methods to an estimation of unknown parameters of the laws of distribution in problems of the theory of reliability. Visnyk Lviv. Univ. Ser. prykl. matem. ta inform. 2002. Vyp. 4. P. 110-113 (in Ukrainian).
  53. Shakhno S.M., Gnatyshyn O.P. Algorithmus für die Lösung eines nichtlinearen Quadratmittelproblems unter Nebenbedingungen. Zeitschrift für Angewandte Mathematik und Mechanik, v.81,2001, suppl. 4, p. 1023-1024.
  54. Shakhno S.M. Some numerical methods for nonlinear least squares problems. Symbolic Aalgebraic Methods and Verification Methods / G.Alefeld, J.Rohn, S.Rump, T.Yamamoto (eds.):, Springer-Verlag/Wien New York, 2001, 235-243.
  55. Shakhno S.M. Some iterative methods for solving nonlinear least squares problems. Symbolic-algebraic Methods and Verification Methods – Theory and Applications / G.Alefeld, J.Rohn, S.Rump, T.Yamamoto (eds.): Dagstuhl-Seminar-Report; 260, 21.11.1999 – 26.11.1999 (99471). Saarbrücken, 2000, p. 24-25.
  56. Dudykevych A.T., Levytska S.M., Shakhno S.M. Practical realization of methods for of boundary problem problems for the ordinary differential equations. Methodical materials. Publishing center Lviv. Univ. 2000. 38 p.(in Ukrainian).
  57. Dudykevych A.T., Levytska S.M., Shakhno S.M. Practical realization of methods of the solving of Cauchy problems for the ordinary differential equations. Methodical materials. Publishing center Lviv. Univ. 2000. 38 p.(in Ukrainian).
  58. Shakhno S.M. Application of methods with successive and parallel approximations to nonlinear least squares problems. Information technologies and systems. 1999, V. 2, No 1. P. 151-154 (in Ukranian).
  59. Shakhno S.M. Investigation of Newton methods in which inner iterative processes are used. Mathematical methods and physico-mechanical fields. 1999. 42. N 1. 39-44 (in Ukranian).
  60. Shakhno S.M., Gnatyshyn O.P. Application of Gauss-Newton method for constrained nonlinear least squares problems. Visnyk Lviv. Univ. Ser. prykl. matem. and inform. 1999. Vyp. 1. P. 255-258 (in Ukrainian).
  61. Tsegelyk G.G., Shakhno S.M. Programming in language the BASIC. Lviv, Lviv Univ., 1999. – 83 p.(in Ukrainian).
  62. Shakhno S.M. , Gnatyshyn O.P. Iterative-Difference Methods for Solving Nonlinear Least-Squares Problem. Progress in Industrial Mathematics at ECMI 98, Verlag B.G.Teubner GMBH, Stuttgart, 1999. 287-294.
  63. Shakhno S.M. , Gnatyshyn O.P. On Some Iterative-Difference Methods for Solving Nonlinear Least-Squares Problem. 10th Conference of the European Consortium for Mathematics in Industry, June 22-27, 1998. Göteborg, Sweden. P. 223-225.
  64. Shakhno S.M. Investigation of difference analogous of Gauss-Newton methods. Matematychni studii. V.10, No 2(1998). P. 119-122.
  65. Shakhno S.M., Nedashkovskyy P.M. Program realization of methods for solving nonlinear least squares problems. Visnyk Lviv. Univ. Ser. mech.-mat 1998. Vyp. 50. P. 211-213 (in Ukrainian).
  66. Shakhno S.M. Approached methods for solving of nonlinear systems of the equations. Publishing centre of Lviv university. The texts of lectures. Lviv, 1998, 32 p. (in Ukrainian).
  67. Dudykevych A.T., Shakhno S.M. Methods for solving of a nonlinear problem about the least squares. Publishing centre of Lviv University. The texts of lectures. Lviv, 1998, 40 p.(in Ukrainian).
  68. Shakhno S.M. Methods with approximation of inverse operator for solving nonlinear least squares problems. “Actual problems of mathematics”. Proceedings of International scientific conf. Part 3. Chernivci-Kyiv (22-27 Juni 1998, Chernivci). P.212-215 (in Ukrainian).
  69. Bartish M.Ya., Shakhno S.M. Investigation of Parametric Iterative Processes for Solving Nonlinear Equations. Problemy upravlenia i informatiki. 1997. N 2. P. 22-30 (Russian).
  70. Bartish M., Shakhno S.M. On the Iterative Steffensen Like Methods. Zeitschrift für Angewandte Mathematik und Mechanik, Berlin, 76(1996) S1. P. 351-352.
  71. Shakhno S.M. Numerical methods for solving nonlinear least squares problems. 9th Conference of the European Consortium for Mathematics in Industry, Technical University of Denmark Lyngby / Copenhagen, Denmark, June 25-29, 1996. P. 543-545.
  72. Shakhno S.M. Investigation of сombination methods for unconstrained minimization of function. Teoretychna elektrotechnika. 1996. Vyp. 53. P. 136-142 (Ukrainian).
  73. Bartish M.Ya., Shakhno S.M., Chypurko A.I. On one modificationGauss-Newton method. Visnyk Lviv. Univ. Ser. mech.-mat. 1995. Vyp. 42. P. 35-38 (in Ukrainian).
  74. Bartish M.Ya., Shakhno S.M. Investigation of Parametric Iterative Processes for Solving Nonlinear Equations. Pattern Recognition and Image Analysis. Vol. 4, No 3, 1994. P. 230-232.
  75. Bartish M.Ya., Shakhno S.M., Lomikovskyy V.O. Numerical investigation of some algorithms for solving nonlinear equations. Visnyk Lviv. Univ. Ser. mech.-mat 1994. Vyp. 41. P. 3-8 (in Ukrainian).
  76. Bartish M.Ya., Shakhno S.M. Investigation of parametric iterative processes for solving nonlinear equations. Proceedings of I International conference of information technologie and systems. 1994. – Vol.1. P.98-99 (in Ukrainian).
  77. Bartish M.Ya., Shakhno S.M. Some methods for solving nonlinear least squares problems. Visnyk Lviv. Univ. Ser. mech.-mat. 1993. Vyp. 39. P. 3-9 (in Ukrainian).
  78. Bartish M.Ya., Shakhno S.M. Finite-difference methods of solving the nonlinear heat-conductivity problem. Journal of Soviet Mathematics. Vol. 65. No 6, August 1993. 1940-1942.
  79. Bartish M.Ya., Shakhno S.M. Generalized Newton-like method for solving nonlinear equations. Visnyk Lviv. Univ. Ser. mech.-mat. 1993. Vyp. 37. P. 3-5 (in Ukrainian).
  80. Shakhno S.M. Convergence conditions of one parametric class of parallel methods for solving systems of nonlinear equations. Visnyk Lviv. Univ. Ser. mech.-mat. 1991. Vyp. 35. P. 79-80 (in Ukrainian).
  81. Baran V.P., Lucyk N.V., Kochubey V.F., Shakhno S.M. Numerical modeling of mixing in narrowed jet flows. Mathem. Physics and Nonlinear Mech. 1990. Vyp. 13(47).(In Russian).
  82. Shakhno S.M. Convergence of one iterative method with successive approximation of inverse operator. Visnyk Lviv. Univ. Ser. mech.-mat. 1989. Vyp. 31. P (in Ukrainian).
  83. Bartish M.Ya., Shakhno S.M. On the Newton method with accelerated convergence. Vestnik Kiev. Universiteta. Modeling and optimization of complex systems. 1987. Vyp. 6.
  84. Shakhno S.M. Der Aufbau und die Forschung einiger Methoden des Newton-Kantorowitsch fur die Losung der nichtlinearen funktionellen Gleichungen. Autoreferat zur Erwerbung des Doktorgrades Physik und Math., Kiev, 1988, 17 s. (in Russian).
  85. Bartish M.Ya., Shakhno S.M. One class of recursive Newton-like methods. Proceedings Union. Seminar “Questions of optimization of calculations “. Kiev. 1987 (in Russian).
  86. Bartish M.Ya., Shakhno S.M. Finite-difference methods of solving the nonlinear heat-conductivity problem. Mathematical methods and physico-mathematical fields. Vol. 25. 1987. P. 25-28 (in Russian).
  87. Senio P.S., Shakhno S.M. Application of some iterative processes for the solving of the equations of gas dynamics. II Symposium on methods of the solving of the nonlinear equations and optimization systems. Tallinn: Valgus, 1981. Proc. and contr. P. 104-106. (in Russian).
  88. Shakhno S.M. About some modifications of Newton method and its applications for solving of problems of gas dynamics. Visnyk Lviv. Univ. Ser. mech.-mat. 1982. Vyp. 19. P (in Ukrainian).
  89. Shakhno S.M. On one method for solving of difference equations of gas dynamics. Visnyk Lviv. Univ. Ser. mech.-mat. 1981. Vyp. 17. P.14-15 (in Ukrainian).
  90. Senio P.S., Shakhno S.M. Solving of difference equations of gas dynamics by Runge method. Visnyk Lviv. Univ. Ser. mech.-mat. 1981. Vyp. 17. P.7-14 (in Ukrainian).
  91. Shakhno S.M., Yarmola H.P. On error estimates for a two-parametric secant for solving nonlinear equations // Mathematical bulletin of NTSH –  – V.9. – P. 375–386. (in Ukrainian).
  92. Shakhno S.M., Yarmola H.P. Two-step secant type method with approximation of the inverse operator // Carpathian Mathematical Publications. – – V. 5, No 1. –  P. 150-155. (in Ukrainian).
  93. Shakhno S. Convergence of the two-step Newton type method for solving of nonlinear equations under the generalized Lipschitz conditions // Physico-mathematcal modeling and information technologies. – – V. 16. –  P.163-172. (in Ukrainian).
  94. Shakhno S.M.Iterative algorithm with convergence order 1,839… under the generalized Lipschitz conditions for the divided differences // Journal of National University “Lvivska poltechnika” “Physical & mathematical sciences. – – V. 740. – P.61-64. (in Ukrainian).
  95. Shakhno S.  Kurchatov method of linear interpolation under the generalized Lipschitz conditions for the first- and second-order divided differences // Visnyk of the Lviv. Univ. Series Mech. Math. – – Issue 77. – P. 235-242. (in Ukrainian).
  96. Shakhno S.  Convergence of combined Newton-secant method and uniqueness of the solution of nonlinear equations // Scientific Journal of the Ternopil national technical university. – – Т. 69,  № 1. –  P. 242-252. (in Ukrainian).
  97. Shakhno S.M., Mel’nyk I.V., Yarmola H.P. Convergence analysis of combined methods for solving nonlinear equations // Mathematical methods and physicomechanical fields– – V. 56,  № 1. –  P.31-39. (in Ukrainian).
  98. Shakhno S.M. Iterative methods for solving nonlinear least squares problems // Journal of Computational & Applied Mathematics. – –№ 1 (111). – P.. 154-169.  (in Ukrainian).
  99. Shakhno S.M., Yarmola H.P.  Two-step method for solving nonlinear equations with nondifferentiable operator // Matematychni Studii – 2011. – V.36, №2. – P.213–220. (in Ukrainian).
  100. Shakhno S., Ubizskyy D., Yarmola H. The use of accelerad Newton method and difference methods for the problem of defining periodic modes in nonlinear dynamical systems // Visnyk of the Lviv. Univ. Series Mech. Math. – 2013. – Issue – P.39-46. (in Ukrainian).

 

Scientific biography

EDUCATION, SCIENCE

2014 Lviv National University, Faculty of Applied Mathematics and Computer Sciences, Professor of Department of Computational Mathematics.
2012 Kyiv National University, Doctor of Physics and Mathematics in speciality “Mathematical modeling and numerical methods” (2012). Dissertation: “Difference and parametric iterative methods for solving nonlinear problems “.
2005 Lviv National University, Faculty of Applied Mathematics and Computer Sciences, Associate Professor of Department of Computational Mathematics.
1991 Lviv National University, Senior scientific researcher in speciality Computational Mathematics
1977-1980 Lviv National University. Doctoral studies in Faculty of Applied Mathematics and Mechanics. Ph. D. in Computational Mathematics, graduated Spring 1988. Advisor: Professor Mykhailo Bartish. Dissertation: “Development and research of some methods of the Newton – Kantorovich type for solving nonlinear functional equations”. Senior scientific researcher (1991).
1972-1977 Lviv National University. Studies in Faculty of Applied Mathematics and Mechanics. Dipl. (equivalent to M.S.) in Applied Mathematics. Advisor: Professor Mykhailo Bartish.

 

 

PERSONAL DATA

Ukrainian. Place and date of birth: Krymne village, Kamin – Kashyrskyi district of Volyn region, 03.11.1953.

 

HONORS AND AWARDS

2010 Universität Innsbruck. Austrian-Ukrainian Cooperation fellowship (Austria) for one month. Advisor: Prof. Dr. Alexander Ostermann.
2003 Universität Wien. Austrian-Ukrainian Cooperation fellowship (Austria) for one month. Advisor: Prof. Dr. Arnold Neumaier.
1999 Universität Karlsruhe. DAAD fellowship (Germany) for two months. Advisor: Prof. Dr. Götz Alefeld.
1995 Member of GAMM (Germany)

 

PROFESSIONAL APPOINTMENTS

2015- Lviv National University. Faculty of Applied Mathematics and Computer Sciences, Professor, Department of Computational Mathematics.
2012 -2015 Lviv National University. Faculty of Applied Mathematics and Computer Sciences, Professor, Department of Computational Mathematics, Vice-dean.
2008 – 2012 Lviv National University. Faculty of Applied Mathematics and Computer Sciences, Associate Professor, Department of Computational Mathematics, Vice-dean.
1994 – 2008 Lviv National University. Faculty of Applied Mathematics and Computer Sciences, Associate Professor, Department of Computational Mathematics.
1987-1994 Lviv National University. Faculty of Applied Mathematics and Computer Sciences, Head of Research Laboratory.
1980-1987 Lviv National University. Engineer, junior scientific researcher, senior scientific researcher of Research Laboratory-63.

 

RESEARCH INTEREST

Numerical methods for solving of nonlinear functional equations, nonlinear boundary value problems, iterative methods for solving optimization problems and nonlinear least squares problems.

 

TEACHING INTEREST

Numerical methods for solving nonlinear functional equations. Iterative solving of nonlinear boundary problems. Numerical methods of linear algebra.

 

SPECIAL SKILLS

Fluent in Ukrainian and Russian, good knowledge of German, satisfactory in English. Experienced in Fortran, Pascal, Linux, Windows, Latex and Matlab.

THESIS DIRECTED

2013
H.P. Yarmola, “Parametric iterative methods of the chord type for solving nonlinear operator equations”. Ph.D. thesis (Computational Mathematics).

 

Projects

Numerical solving of direct and inverse problems of mathematical physics and mechanics by projection and grid methods :Report on research work; DR No. 0112U001285; Inv. No. 0212U004222 – Lviv, LNU, 2013 – 340 p.

Awards

Academician of the Academy of Sciences of the Higher School of Ukraine, 2016

Teaching materials

Practice on numerical methods of linear algebra

Typical problems of numerical methods of linear algebra 2018

Шахно С.М. Чисельні методи лінійної алгебри. Навчальний посібник. Видав. центр ЛНУ ім. І.Франка, 2007. 246 с. (З грифом МОН України).

Дудикевич А.Т., Левицька С.М., Шахно С.М. Практична реалізація методів розв’язування нелінійних рівнянь і систем рівнянь. Навчальний посібник. Видав. центр ЛНУ ім. І.Франка, 2007. 78 с.98.

Шахно С.М., Дудикевич А.Т., Левицька С.М. Практична реалізація чисельних методів лінійної алгебри. Навчальний посібник. Видав. центр ЛНУ ім. І.Франка, 2008. 144 с. (З грифом МОН України).

Шахно С.М., Дудикевич А.Т., Левицька С.М. Практикум з чисельних методів Навчальний посібник. Видав. центр ЛНУ ім. І.Франка, 2013. 435 с. (З грифом МОНмолодьспорту України).

Дудикевич А.Т., Левицька С.М., Шахно С.М. Практична реалізація методів розв’язування крайових задач для звичайних диференціальних рівнянь. Методичні матеріали. Львів. Видавничий центр ЛНУ ім. Івана Франка. 2000. 38 с.

Дудикевич А.Т., Левицька С.М., Шахно С.М. Практична реалізація методів розв’язування задач Коші для звичайних диференціальних рівнянь. Методичні матеріали. Львів. Видавничий центр ЛНУ ім. Івана Франка. 2000. 38 с.

Дудикевич А.Т., Левицька С.М., Шахно С.М. Практична реалізація методів чисельного інтегрування. Методичні вказівки. Видавн. центр ЛНУ ім. І.Франка. 37 с.

Шахно С.М. Методи розв’язування нелінійної задачі про найменші квадрати. Видавничий центр Львів. ун-ту. Тексти лекцій. ТЛ N 3./98, Львів,1998, 40 с.

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