Modified Runge-Kutta method

Modern Runge-Kutta method of solving ODE bears a slight resemblance with the classical (explicit) method and is based on the transformation of the differential equation to the integral one. The contents of the mathematical theory was formulated by J.C. Butcher et all. Nevertheless, the technique of constracting fundamental equations of RK-method...

kuznecov.pdf6.04 MB

On the domain decomposition method for parabolic problems

The paper deals with studying the domain decomposition algorithm with overlapping subdomains. This algorithm is based on the splitting method and uses the additive presentation of some bilinear form. Earlier this method was described for two subdomains. In our consideration we formulate the decomposition algorithm for an arbitrary number of...

laevskiy.pdf6.04 MB

Variational rational splines of many variables

The purpose of this paper is to construct the interpolating function as a ratio of two splines. The numerator and the denominator of this ratio minimize some combined variational functional on the set of pairs of functions which satisfy interpolating conditions and some additional restrictions. Such a construction was proposed...

rozhenko.pdf5.97 MB