On the stability of an explicit difference scheme for hyperbolic equation with integral conditions

Abstract

On the stability of an explicit difference scheme for hyperbolic equation with integral conditions. The aim of the work is stability analysis of solution of finite difference method for hyperbolic equations. Trying to achieve formulated aim these tasks were solved: • a method of transformation of three-layered finite difference scheme into two-layered one was investigated; • a spectrum of transition matrix subject to the properties of second order differential operator Lambda was studied; • stability conditions of hyperbolic type equations with nonlocal conditions subject to boundary parameters were obtained; • numerical experiments, confirming theoretical derivations were made. Derived results could be used to solve one-dimensional tasks with hyperbolic equations in different sciences, to analyse spectrum structure of mathematical models and construct new numerical methods for solving hyperbolic PDEs