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EXAMPLES OF EXACT CONSTRUCTION OF GEOMETRICALLY OPTIMAL TWO-DIMENSIONAL GRIDS

A.F. Sidorov
VANT. Ser.: Mat. Mod. Fiz. Proc 1994. Вып.4. С. 18-22.

      Classes of exact solutions were derived for Euler-Ostrogradsky’s equations, corresponding to non-linear combined functional, with the help of which regular curvilinear grids, close to uniform and ortogonal ones are constructed. In general case, the above mentioned classes are described by the system of ordinary differential equations of the 8-th order for which the problem of Cauchy is posed. In a specific symmetric case the system is reduced to one non-linear equation of the 4-th order, which has been integrated to the end in quadratures. The influence of the weight in terms of the functional responsible for orthoganality on quality of grids has been investigated. The results of numerical calculations are given. The constructed solutions may, for example, serve as tests for investigation of different numerical methods for grid generation.










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