A polynomial approximation of nonlinear algebraic equations of the mathematical physics

Abstract

In the work on the basis of the ideas and results of V. K. Dzyadyk and V. L. Makarov high–exact numerical–analytical algorithms for solving algebraically–nonlinear equations of mathematical physics are constructed and theoretical grounded. Two mutually complemented algorithm (approximating without the satiation of exactness and spline–algorithm) for solving such equations are proposed. Using parabolic spline allowed to construct a monotone difference scheme for the equation of convection–diffusion. The results of computational experiments in the event of significant advantages over convection diffusion are considered.