On increasing the accuracy of difference schemes when calculating centered rarefaction waves

A method is proposed that makes it possible to increase the accuracy of shock capturing numerical schemes inside centered rarefaction waves arising as a result of the discontinuity decay in the initial data of the approximated Cauchy problem for a hyperbolic system of conservation laws. This method is based on the condensation of the numerical grid at a certain initial time interval of the considered problem. Test calculations of the special Cauchy problem for a shallow water equations are presented, demonstrating the capabilities of this method.