Construction of algebraic-analytic discrete approximations for linear and nonlinear hyperbolic equations in R^{2}. Part I

Mirosław Luśtyk; Mykola Prytula

Opuscula Math. 27, no. 1 (2007), 25-36

Opuscula Mathematica

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

Abstract. 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.

Keywords: algebraic-analytic approximation, d'Alembert type formula, Riemann functions, fixed point problem.

Mathematics Subject Classification: 35B05, 65F05.

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About the authors

Mirosław Luśtyk
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza, 30, 30-065 Cracow, Poland

Mykola Prytula
Ivan Franko National University in L'viv, Dept. of Applied Mathematics and Informatics, Universytetska str. 1, L'viv, 79000, Ukraine

About the article

Received: 2006-11-23.

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

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