Construction of algebraic-analytic discrete approximations for linear and nonlinear hyperbolic equations in R2. Pt. 1

• Autorzy: Luśtyk M. , Prytula M.
• Języki publikacji: EN

Abstrakty

EN

An algebraic-analytic method for constructing discrete approximations of linear hyperbolic equations based on a generalized d'Alembert formula of the Lytvyn and Riemann expressions for Cauchy data is proposed. The problem is reduced to some special case of the fixed point problem.

Słowa kluczowe

EN

algebraic-analytic approximation; d'Alembert type formula; Riemann functions; fixed point problem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2007
• Tom: Vol. 27, no. 1
• Strony: 25--36
• Opis fizyczny: Bibliogr. 6 poz., wykr..

Twórcy

autor

Luśtyk M.

autor

Prytula M.

• AGH University of Technology, Faculty of Applied Mathematics, al. Mickiewicza, 30, 30-059 Cracow, Poland,

Bibliografia

• [1] O.M. Lytvyn, Numerical methods: supplementing chapters, Naukowa Dumka, Kiev, 2005, (in Ukrainian).
• [2] O.M. Lytvyn, Interpolation of functions and its applications, Osnowa, Charkov, 2002, (in Ukrainian).
• [3] W.S. Wladimirow, Equation of Mathematical Physics, Nauka, Moscow, 1976.
• [4] M. Luśtyk, O. Bihun, Approximation properties of the Lie-algebraic scheme, Matematychni Studii 20 (2003), 85-91.
• [5] M. Luśtyk, The Lie-Algebraic Discrete Approximation Scheme for Evolution Equations with Dirichlet/Neumann Data, Universitatis Iagellonicae Acta Mathematica 40 (2002), 117-124.
• [6] Yu. A. Mitropolski A.K. Prykarpatsky, V.H. Samoilenko, A Lie-algebraic scheme of discrete approximations of dynamical systems of mathematical physics, Ukrainian Math. Journal 40 (l988), 453-458.