The stimulus for the present work is the growing need for more accurate numerical methods. The rapid advances in computer technology have not provided the resources for computations which make use of methods with low accuracy. The computational speed of computers is continually increasing, while memory still remains a problem when one handles large arrays. More accurate numerical methods allow us to reduce the overall computation time by of magnitude. several orders The problem of finding the most efficient methods for the numerical solution of equations, under the assumption of fixed array...

The problems of ocean dynamics present more and more com plex tasks for investigators, based on the continuously sophisti cation of theoretical models, which are applied with the help of universal and efficient algorithms of numerical mathematics. The present level of our knowledge in the field of mathemat ical physics and numerical mathematics allows one to give rather complete theoretical analysis of basic statements of problems as well as numerical algorithms. Our task is to perform such analy sis and also to analyze the results of calculations in order to improve our knowledge of the...

This monograph is devoted to urgent questions of the theory and applications of the Monte Carlo method for solving problems of atmospheric optics and hydrooptics. The importance of these problems has grown because of the increas- ing need to interpret optical observations, and to estimate radiative balance precisely for weather forecasting. Inhomogeneity and sphericity of the atmos- phere, absorption in atmospheric layers, multiple scattering and polarization of light, all create difficulties in solving these problems by traditional methods of computational mathematics. Particular difficulty...

The present volume is an adaptation of a series of lectures on numerical mathematics which the author has been giving to students of mathematics at the Novosibirsk State University during the span of several years. In dealing with problems of applied and numerical mathematics the author sought to focus his attention on those complicated problems of mathe- matical physics which, in the course of their solution, can be reduced to simpler and theoretically better developed problems allowing effective algorithmic realization on modern computers. It is usually these kinds of problems that a young...