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

By Karlos J. Kachiashvili

The consequences mentioned during this publication are fascinating and invaluable for quite a lot of experts and scientists operating within the box of utilized arithmetic, and within the modelling and tracking of toxins of ordinary waters, ecology, hydrology, strength engineering and development of alternative buildings of water gadgets. Their value and useful price are submitted within the pleasant shape for comprehension and are prepared for direct software for the answer of sensible initiatives. benefits of the elaborated equipment and algorithms are proven not just via theoretical decisions and calculations, but additionally in the course of the demonstration of result of specific calculus and modelling.

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Let us designate (for given value t ): 2  lau ( x )   (t   , x );  last ( x )   (t , x ); t '  t   ; ˆ lau    ˆ (t ' )  f lau ( x )  f (t , x )  ˆlau 1 1  D (t , x )  Iˆ; D (t , x )   last ( x )  (1   )  ˆ (t ' )  last ( x );   ˆ (t   );  lau   (t   , x ). 7)) and the boundary conditions ˆ lau  lau ( x )   lau ( x ) .  . 2. Reduction of the multi-dimensional diffusion equation to the one-dimensional. Described below algorithm of solution of diffusion equation is used in multi-dimensional problems and is an alternative to the considered above algorithms.

Y. 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].

The vector composed by spatial co-ordinates, here we shall designate by r  [ x, y, z] . 2, the domain of change of variables x , y , z , is defined by conditions 0~ x   ;  r ( x)  y  l ( x) ; 0  z  H ( x, y) , then replacement of variables by formulae ~ x  x; ~y  W0   y   r ( x)  ; ~z  H 0  z , H ( x, y ) l ( x)   r ( x) where W0 , H 0  const , leads to required transformation of the domain G : the domain of y , ~z , is the parallelepiped change of variables ~ x,~ 0~ x  ; ~ z  H0 .

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