Modification of the Lie-algebraic scheme and
approximation error estimations

O. H. Bihun

A new modification of the Lie-algebraic scheme for solving partial differential equations with initial and boundary conditions based on constructing quasirepresentations of the Heisenberg-Weyl algebra operators involving boundary conditions is proposed. Approximation errors for the modified scheme are evaluated.

1. Bihun O., Luśtyk M. Numerical tests and theoretical estimations for a Lie-algebraic scheme of discrete approximations, Visnyk of the Lviv University. Series Applied Mathematiсs and Computer Science. 6 (2003)(to appear).

2. Bihun O. H., Luśtyk M. S. Approximation properties of the Lie-algebraic scheme, Matematychni Studii 20 (2003), № 1, 85–91.

3. Calogero F., Franco E. Numerical tests of a novel technique to compute the eigenvalues of differential operators, Il Nuovo Cimento 89B (1985), no 2, 161–208.

4. Luśtyk M. Lie-algebraic discrete approximation for nonlinear evolution equations, Mathematical Methods and Physicomechanical Fields 42 (1999), no 1, 7–10.

5. Marcinkowska H. Dystrybucje, przestrzenie Sobolewa, równania rózniczkowe, Wydawnictwo Naukowe PWN, Warszawa, 1993.

6. Митропольский Ю. А., Прикарпатский А. К., Самойленко В. Гр. Алгебраическая схема дискретных аппроксимаций линейных и нелинейных динамических систем математической физики, Укр.мат.журн. 40 (1988), № 4, 453–458.

7. Самойленко В. Гр. Алгебраическая схема дискретных аппроксимаций динамических систем математической физики и оценки её точности, Асимптотические методы в задачах мат. физики. Киев, Институт математики АН УССР, 1988. С.144–151.

	Modification of the Lie-algebraic scheme and approximation error estimations
Author	O. H. Bihun Department of Applied Mathematics and Computer Science, Lviv Ivan Franko National University
Abstract	A new modification of the Lie-algebraic scheme for solving partial differential equations with initial and boundary conditions based on constructing quasirepresentations of the Heisenberg-Weyl algebra operators involving boundary conditions is proposed. Approximation errors for the modified scheme are evaluated.
Keywords	Lie-algebrais scheme, approximation error estimation, Heisenberg-Weyl algebra operator
DOI	doi:10.30970/ms.20.2.179-184
Reference	1. Bihun O., Luśtyk M. Numerical tests and theoretical estimations for a Lie-algebraic scheme of discrete approximations, Visnyk of the Lviv University. Series Applied Mathematiсs and Computer Science. 6 (2003)(to appear). 2. Bihun O. H., Luśtyk M. S. Approximation properties of the Lie-algebraic scheme, Matematychni Studii 20 (2003), № 1, 85–91. 3. Calogero F., Franco E. Numerical tests of a novel technique to compute the eigenvalues of differential operators, Il Nuovo Cimento 89B (1985), no 2, 161–208. 4. Luśtyk M. Lie-algebraic discrete approximation for nonlinear evolution equations, Mathematical Methods and Physicomechanical Fields 42 (1999), no 1, 7–10. 5. Marcinkowska H. Dystrybucje, przestrzenie Sobolewa, równania rózniczkowe, Wydawnictwo Naukowe PWN, Warszawa, 1993. 6. Митропольский Ю. А., Прикарпатский А. К., Самойленко В. Гр. Алгебраическая схема дискретных аппроксимаций линейных и нелинейных динамических систем математической физики, Укр.мат.журн. 40 (1988), № 4, 453–458. 7. Самойленко В. Гр. Алгебраическая схема дискретных аппроксимаций динамических систем математической физики и оценки её точности, Асимптотические методы в задачах мат. физики. Киев, Институт математики АН УССР, 1988. С.144–151.
Pages	179-184
Volume	20
Issue	2
Year	2003
Journal	Matematychni Studii
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Table of content of issue	html

Modification of the Lie-algebraic scheme and approximation error estimations