Advanced Modeling and Computer Technologies for Fluvial by Karlos J. Kachiashvili

By Karlos J. Kachiashvili

The implications mentioned during this booklet are attention-grabbing and important for a variety of experts and scientists operating within the box of utilized arithmetic, and within the modelling and tracking of toxins of common waters, ecology, hydrology, strength engineering and development of other buildings of water items. Their value and sensible worth are submitted within the pleasant shape for comprehension and are prepared for direct software for the answer of useful initiatives. merits of the elaborated tools and algorithms are proven not just via theoretical decisions and calculations, but additionally throughout the demonstration of result of specific calculus and modelling.

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55)     ,   is the integral part from division. e. at a point within the ~ where i   1 2 controlled range. h1 , y k , z m , t     h1  that has accuracy O(h1 ) , x i  1 ,x i are the nearest grid nodes for . Note 2. 55), a modification of the method of scrolling or of the factorization method is used. 6. OPTIMIZATION PROBLEMS OF THE ALGORITHMS CONNECTED WITH DIFFERENCE SCHEMES Let us consider problems of optimum choice of the parameters of the algorithm at practical realization of difference schemes [38, 40].

If the number of known coordinates of the contour points is not great enough, it is possible to solve the above mentioned problem in the following way. Let us represent the initial curve in the parametric form x   1 (t ); y   2 (t ), where t is the length of the polygon line connecting the current point of the curve with all previous nodes. The functions  1 (t ) and  2 (t ) can be approximated by cubical splines [16]. 1. 4 is already possible. For example, if we increase the number of nodes of the reviewed above sinusoid using above described method, inserting three additional nodes between each adjacent points, the approximating curve practically will merge with the given sinusoid.

E. p j  P0 , then auxiliary solutions of the considered equation of diffusion, about which was spoken in the previous Item, can be defined as follows: u 0  1; u j  1 / P0 . In future the value s0 we shall call the average concentration. Results of the numerical solution of the equation of diffusion can be compared to it. In following two Items the generalization of known, often used method of linear interpolation of the function of one real variable for the case, when the function of two or Deterministic Mathematical Models of Pollutants Transfer in Rivers 21 three variables is considered, is given.

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