Application of the generalized method of Lie-algebraic discrete approximations to the solution of the Cauchy problem with the advection equation

Abstract

The approximation properties and the conditions of convergence of a computational scheme of the generalized method of Lie-algebraic discrete approximations for the solution of the Cauchy problem with a one-dimensional advection equation are proved. The reduction of the Cauchy problem with the advection equation to a system of linear algebraic equations ensures the factorial convergence in all variables of the equation.