By Karlos J. Kachiashvili

ISBN-10: 1614700184

ISBN-13: 9781614700180

The implications mentioned during this publication are attention-grabbing and valuable for quite a lot of experts and scientists operating within the box of utilized arithmetic, and within the modelling and tracking of pollutants of traditional waters, ecology, hydrology, strength engineering and development of other constructions of water gadgets. Their value and sensible worth are submitted within the pleasant shape for comprehension and are prepared for direct software for the answer of functional initiatives. merits of the elaborated equipment and algorithms are proven not just via theoretical decisions and calculations, but in addition throughout the demonstration of result of specific calculus and modelling.

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**Sample text**

42) and have a simple geometrical sense: the point P with given coordinates lies on the normal to the curve passing through its point P 0 , corresponding to the value of the parameter equal to , and apart from the point P 0 on the distance , and 24 Karlos J. Kachiashvili and D. Y. 2). 2. Curvilinear coordinates connected with the line. then functions a( ) and b( ) can be determined from the condition of orthogonality of the curvilinear coordinate system taking into account that in this case nondiagonal components of the covariant metric tensor are equal to g12 (1 ( ) a ( ) ) a( ) (2 ( ) b( ) ) b( ) 1 ( ) a( ) 2 ( ) b( ) d a( ) b( ) .

Ax means that ˆ is equal to the sum of m operators, each of which contains the derivatives only by one variable. The difference operator ˆ h , Diagonality of the tensor approximating ˆ , also can be presented in the form of the sum of one-dimensional difference operators, the expressions for which can be derived from the corresponding formulae of the previous item. 2. Diffusion Equation In the so-called mixed problem containing the diffusion equation, unknown function t , x is considered defined at t 0 and x X , where X is the interval (in the one- dimensional problem) or the region (in the multivariable problem).

N ), where h b a / N . The matrix of this system is three diagonal and, accordingly, the system of equations can be solved by the method of direct scrolling. The substitution of the classical boundary conditions in the point b by non classical conditions is equivalent to the substitution of the latest equation in the given system by linear ratio between the values of the function x in the point b and some internal point of the interval X . Such system of equations is solved by the special scrolling method [43].

### Advanced Modeling and Computer Technologies for Fluvial Water Quality Research and Control by Karlos J. Kachiashvili

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