Generalized method of Lie-algebraic discrete approximations for solving Cauchy problems with evolution equation

• Autorzy: Kindybaliuk A.
• Języki publikacji: EN

Abstrakty

EN

We consider solving the Cauchy problem with an abstract linear evolution equation by means of the Generalized Method of Lie-algebraic discrete approximations. Discretization of the equation is performed by all variables in equation and leads to a factorial rate of convergence if Lagrange interpolation is used for building quasi representation of differential operator. The rank of a finite dimensional operator and approximation properties have been determined. Error estimations and the factorial rate of convergence have been proved.

Słowa kluczowe

EN

generalized method of Lie-algebraic discrete approximations; dynamical systems; evolution equation; finite dimensional quasi representation; approximations; Lagrange’s polynomial; factorial convergence

PL

układy dynamiczne; aproksymacje; wielomian Lagrange'a

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 2
• Strony: 51--62
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Kindybaliuk A.

• Ivan Franko National University of Lviv, Lviv, Ukraine

Bibliografia

• [1] Mytropolskii Yu.A., Prykarpatskii A.K., Samojlenko V.Hr., Algebraic scheme of discrete approximations of linear and nonlinear dynamical systems of mathematical physics, Ukrainian Mathematical Journal 1988, 40, 453-458.
• [2] Calogero F., Interpolation, differentiation and solution of eigenvalue problems in more than one dimension, Lett. Nuovo Cimento. 1983, 38, 13, 453-459.
• [3] Bihun O., Prytula M., Method of Lie algebraic discrete approximations in the theory of dynamical systems, 2004, 1, 24-31 (in Ukrainian).
• [4] Bihun O., Prytula M., The rank of projection-algebraic representations of some differential operators, Matematychni Studii 2011, 35, 1, 9-21.
• [5] Kindybaliuk A.A., Prytula M.M., Generalization of scheme of the Lie-algebraic method of discrete approximations for Cauchy problem, XIX Ukrainian Conference of Contemporary Problems of Applied Mathematics and Informatics, L’viv 2013, 73-74 (in Ukrainian).
• [6] Horn R.A., Johnson C.R., Matrix Analysis, Cambridge University Press, Cambridge 1990.
• [7] Trenogin V.A., Functional Analysis, Fizmatlit, Moscow 2002 (in Russian).
• [8] Berezin I.S., Zhydkov N.P., Numeric Methods, Vol. 1, Fizmatgiz, Moscow 1962 (in Russian).
• [9] Richtmayer R., Difference Methods of Solving Boundary-value Problems, Mir, Moscow 1972 (in Russian).
• [10] Liusternik L.A., Sobolev V.I., Elements of Functional Analysis, Nauka, Moscow 1965 (in Russian).
• [11] Samojlenko V.Hr., Algebraic Scheme of Discrete Approximations of Mathematical Physics and its Precision Estimations. Asymptotic Methods in Math. Physics, Mathematics Institute AN USSR, Kyiv 1988, 144-151 (in Russian).