Coefficients and norms of error functionals of optimal difference formulas
Annotatsiya
In this paper, we consider the problem of constructing optimal difference formulas for an approximate solution to the Cauchy problem in the Sobolev space of functions of the m-th order derivatives (in the generalized sense) are square integrable. Using a discrete analogue of a differential operator of the first order, one can find representations of optimal difference formulas. In the first section, we consider the construction of optimal explicit difference formulas of the Adams type. Here, minimizing the norm of the error functional with respect to the coefficients, a system of linear algebraic equations is obtained. This system is reduced to a system of convolution equations. And it is completely solved using a discrete analogue of a second-order differential operator.