Difference schemes with variable weights for hyperbolic systems of equations

Rezults of the difference schemes with wariable weights stability investigation for the systems of linear hyperbolic equations are considered. Stability estimates with respect to initial data and right sides are obtained in such norms that correspond to convergence of difference schemes with compound grids for hyperbolic equations in the case of wariable and discontinuity weight functions. Rezults of mathematical modelling of decay break problem with the help of time-adaptive grid are considered.