Mathematics |
|
 |
2007, No. 2
A.A. Abdrakhmanova
A SPLINE METHOD VARIANT FOR BEAMS BENDING
A numerical solution method for differential equation of the fourth order is considered, describing a bending of a beam. A spline-method in the integrated form, basing on spline-functions of the fifth degree and providing sixth order of convergence, is discussed. For estimation of accuracy of the considered method a modelling problem having the exact analytical solution is used.
A.A. Abdrakhmanova, V.P. Pavlov
MATHEMATICAL MODELLING OF STRESS-STRAIN STATE OF A ROD AT LARGE DEFORMATIONS
In this paper a method of deriving equilibrium equations for the case of geometrical nonlinearity without restrictions on a magnitude of deformations is developed. Numerical method of finding approximate solution is worked out. Model problem which has exact solution is formulated and above procedure is used for approximate solving the problem. Comparison of exact and approximate solutions shows high accuracy of the proposed numerical method.
M. Andramonov
PROBLEMS OF QUASI-LINEAR ALGEBRA
In the paper problems of quasi-linear algebra are considered. Linear programming problems with logical conditions are resolved. Double branching is used in order to find exact or approximate solutions of such problems. The results can be applied to complicated problems of quasi-differential and co-differential analysis.
M.N. Bardina
In the paper vertical streams one-dimensional problems are studied. Exact solutions are constructed by methods of a running wave, division of variables, similarity and others. The obtained analytical solutions permit to make conclusions of the common character, to predict dynamics of processes and can be used as a basis for ”test” tasks for checking the correctness and to estimating of accuracy of numerical methods.
T.A. Sribnaya
UNIFORM EXHAUSTION OF A FAMILY OF WEAKLY REGULAR OUTER VEKTOR MEASURES
Conditions for the unifom exhaustion of a family of weakly regular k-outer measures defined on an algebra of sets containing the class of open subsets of some ?-topological space (T, ?) and taking values in topological abelian group are found.
N.R. Pinigina, S.V. Popov
The solvability of the boundary-value problem for the second order parabolic equations with various time conditions in Holder spaces is considered. We show that the Holder classes of the solutions depend significantly on the from of the gluing conditions and non-integral H?older exponent.