2022 Issue №1

In this paper we conceder the properties of the tangential incomplete block LU — decomposition. We present an analytical approach for determination of the optimal values of the decomposition parameter and derive sharp estimates of the convergence rate for a broad class of model problems. Numerical results prove that high convergence rate can be achieved by using these values also for the problems with varying coefficients.

To achieve an optimum temperature of rocket fuel, its negative temperature and the amount of its purification from impurities are necessary. For this purpose, a mathematical model of the temperature dependence inside the bubbler has been developed in this article.

In this paper, the most characteristic errors in the application of mathematical-statistical and model methods that periodically occur during the review of scientific geological journals were analyzed, and recommendations for their elimination were given. The problems of determining relative errors in simplified mathematical models are discussed. The necessity of calculating the parameters of the background value and excluding its influence on the calculation of the “useful signal” is shown. A graphical method for determining the minimum abnormal content is also proposed for discussion and testing.