On numerical solution of the Dirichlet problem by the method of locally-canonical decomposition.
On Numerical Solution of the Gardner–Ostrovsky Equation
A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation (ut + cux + α uux + α1u2ux + βuxxx)x = γu which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth’ rotation. Particular versions of this equation with zero some of coefficients, α, α1, β, or γ are also known in numerous applications....
On numerical solution of weight minimization of elastic bodies weakly supporting tension
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its weight and to the hydrostatic pressure. A part of the boundary has to be found so as to minimize a given cost functional. The numerical realization using a penalty method and finite element technique is presented. Some typical results are shown.
On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method
In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.
On numerical solutions of partial differential equations by the decomposition method
On one approach to local surface smoothing
A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.
On one method of numerical integration
The uniform convergence of a sequence of Lienhard approximation of a given continuous function is proved. Further, a method of numerical integration is derived which is based on the Lienhard interpolation method.
On one system of nonlinear equations
On optimal center locations for radial basis function interpolation: computational aspects.
On Optimal Chebyshev-Type Quadratures.
On Optimal Extreme-Discrepancy Point Sets in the Square.
On Optimal Global Error Bounds Obtained by Scaled Local Error Estimates.
On optimal methods in numerical analysis
Round-off error analysis of the gradient method.
On optimal nodal splines and their applications.
On optimal quadrature formulae.
On optimal regularization methods for fractional differentiation.
On optimal triangular meshes for minimizing the gradient error.
On optimizing a maximin nonlinear function subject to replicated quasi-arborescence-like constraints.
In this paper we present the motivation for using the Truncated Newton method in an algorithm that maximises a non-linear function with additional maximin-like arguments subject to a network-like linear system of constraints. The special structure of the network (so-termed replicated quasi-arborescence) allows to introduce the new concept of independent superbasic sets and, then, using second-order information about the objective function without too much computer effort and storage.
On order 5 symplectic explicit Runge-Kutta Nyström methods.
On orthogonal decomposition of two-dimensional vector fields