Application of generalized method of Lie algebraic discrete approximations for solving Cauchy problem with heat transfer equation (in Ukrainian)

1. I.S. Berezin, N.P. Zhydkov, Numerical methods, V.1, M: Fismathyz, 1962. (in Russian)

2. O. Bihun, M. Prytula, The method of Lie algebraic discrete approximations in the theory of dynamical systems, Mat. Visnyk NTSH, 1 (2004), 24–31. (in Ukrainian)

3. A.A. Kindybaliuk, M.M. Prytula, Generalization of the scheme of the Lie algebraic discrete approximations for Cauchy problem, XIX National ukrainian scientific conferece: Modern problems of applied mathematics and informatics. Theses. L’viv, (2013), 73–74. (in Ukrainian)

4. L.A. Liusternik, V.I. Sobolev, Elements of functional analysis, М.: Nauka, 1965. (in Russian)

5. M. Lustyk, A. Prykarpatski, M. Prytula, M. Vovk, Functional-operator analysis of converegence problems for F.Calogero’s method of discrete approximations in Banach spaces, Math. Visnyk NTSH, 9 (2012), 168–179. (in Ukrainian)

6. Ya A. Mytropolski, A.K. Prykarpatski, V.Hr. Samoylenko, Algebraic scheme of discrete approximations of linear and nonlinear dynamical systems of mathematical phisics, Ukr. Mat. Journ., 40 (1988), 453–458. (in Russian)

7. R. Richtmyer, Difference methods for solving boundary-value problems, М.: Mir, 1972. (in Russian)

8. А.А. Samarskii, А.V. Gulin, Numerical methods: Handbook for students, М.: Nauka, 1989. (in Russian)

9. V.Hr. Samoylenko, Algebraic scheme of discrete approximations for dynamical systems of mathematical phisics and estimations of its precision, Asymptotic methods in math-phisics problems К.: Mathematical institute АN USSR, (1988), 144–151. (in Russian)

10. V.A. Trenogin, Functional analysis, М: FIZMATLIT, 2002. (in Russian)

11. O.H. Bihun, Approximation properties of the Lie-algebraic scheme, Mat. Stud., 20 (2003), №1, 85–91.

12. O.H. Bihun Modification of the Lie-algebraic scheme and approximation error estimations, Mat. Stud., 20 (2003), №2, 179–184.

13. O.H. Bihun, M. Lustyk, Numerical tests and theoretical estimations for a Lie-algebraic scheme of discrete approximations, Visnyk of the Lviv University. Series of Applied Mathematics and Computer Science, 6 (2003), 3–10.

14. O. Bihun, M. Prytula, The rank of projection-algebraic representations of some differential operators, Mat. Stud. 35 (2011), №1, 9–21.

15. F. Calogero, Interpolation, differentiation and solution of eigenvalue problems in more than one dimension, Lett. Nuovo Cimento, 38 (1983), №13, 453–459.

16. F. Calogero, E. Franko, Numerical tests of a novel technique to compute the eigen values of differential operators, Il Nuovo Cins., 89 (1985), №2, 161–208.

17. F. Casas, Solution of linear partial differential equations by Lie algebraic method, Journ. of Comp. Appl. Math., 76 (1996), 159–170.

18. R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge: Cambridge University Press, 1990.

19. M. Lustyk, Lie-algebraic discrete approximation for nonlinear evolution equations, Journ. of Mathem. Sc., 109 (2002), №1, 1169–1172. 20. M. Lustyk, The Lie-algebraic discrete approximation scheme for evolution equations with Dirichlet/ Neumann data, Universitatis Iagellonicae Acta Mathematica, 40 (2002), 117-124.

21. A.K. Prykarpatsky, M.M. Prytula, O.O. Yerchenko, The Lie-algebraic discrete approximations in computing analysis, Volyn Mathematical Bulletin, 3 (1996), 113–116.

22. J. Wei, E. Norman, On global representations of the solution of linear differential equations as a product of exponentials, Proc. Amer. Math. Soc., 15 (1964), 327–334.

23. F. Wolf, Lie algebraic solutions of linear Foker-Plank equations, Journ. Math. Phys., 29 (1988), 305–307.