A method of parametric correction of difference schemes

Abstract

The difference discretization of problems of mathematical physics can be performed in different ways, so that manifolds of d.s. arise which may be used for obtaining specific properties such as conservativeness, stability, economy, or a certain order of approximation, etc. We know, however, that A-stability cannot be obtained simultaneously with e.g., the third or higher order of approximation of stiff systems of equations in the class of linear implicit schemes,ormonotonicity simultaneously with second or higher order of approximation for hyperbolic equations in the class of linear d.s. , or stability simultaneously with second or higher order of approximation in the class of explicit schemes for the equations of gas dynamics in Euler variables. We shall consider an approach whereby these difficulties can be to some extent overcome and d.s. with new properties obtained.