Skew-Symmetric Difference Analogs of the Fourth-Order Approximation to the First Derivative

Abstract: Assume that we have an initial–boundary value problem for a system of first-orderhyperbolic equations that has an integral conservation law. One of the options for the numericalsolution of this kind of a problem is the construction of a difference scheme for spatial variables,followed by the solution of the resulting system of ordinary differential equations. For the stabilityof the solution of this ODE system, it is desirable that it has a first integral that is an analog ofthe conservation law for the original problem. An antisymmetric difference analog of the firstderivative of the fourth-order approximation is constructed for this purpose. © 2022, Pleiades Publishing, Ltd.