Home – Home – Jornals – Numerical Analysis and Applications 2015 number 1

Computing of time-optimal inertial control amounts to solving the three problems: 1) computing of optimal control on the assumption that the control is without inertia; 2) finding the optimal switching time of the control; 3) calculating of the error induced by the time lag of the control followed by correcting the control time and switching moments. Characteristics of the problems are considered and methods of their solution are given. A way of assignment of initial approximation is presented. A computational algorithm, results of modeling and numerical computations are performed.

The problems of the numerical analysis of stochastic differential equations with oscillatory solutions trajectories are studied. For the analysis of the numerical solution it is proposed to use the frequency response of generalizing the integral curve and the phase portrait. The results of numerical experiments carried out on a cluster of NCC-30T Siberian Supercomputer Center at the ICM\&MG SB RAS using a set of programs PARMONC are presented.

In this paper, the response of the general atmosphere circulation to the climate changes is simulated with use of a medium complexity model. It is shown that with a temperature gradient decrease, the Hadley circulation weakens and its boundary moves to the poles. The troposphere height dynamics depending on atmosphere temperature is investigated. A relation between characteristics determining the atmosphere baroclinic instability is obtained.

This paper discusses several automated methods of acceleration programs. The acceleration is achieved by parallelization and optimization of memory access. Optimization of accesses to RAM is achieved by switching to a block code and block placements arrays. When using a distributed memory, the automated distribution of arrays and array distribution with overlapping are employed. Automation is implemented using the C language with pragmas in Open Parallelizing System. This paper presents the numerical results for linear algebra and mathematical physics. Some features of this demonstration converter have a remote access to the Internet.

The conditions using the inverse operator and its form in the truncated two-dimensional convolution operators on sets with smooth boundaries are known. The presence of the corner points adds complexity to the task. The equations with multi-dimensional convolution operators on polyhedra is considered. The approximate method for them is proposed, and estimates for the errors are obtained. The possibility of approximation solutions of these equations with multi-dimensional cyclic matrices is also investigated.

In this paper, we discuss a new coupled reduced alternating group explicit (CRAGE) and Newton-CRAGE iteration methods to solve non-linear singular two point boundary value problems u″ = ƒ(r,u,u′), 0< r<1, subject to given natural boundary conditions u(0) = A₁, u(1) = A₂, where A₁ and A₂ are finite constants, along with a third order numerical method on a geometric mesh. The proposed method is applicable to singular and non-singular problems. We discuss the convergence of the CRAGE iteration method in detail. The results obtained from the proposed CRAGE iteration method are compared with the results of the corresponding two parameter alternating group explicit (TAGE) iteration methods to demonstrate computationally the efficiency of the proposed method.

A new iterative algorithm is suggested for calculating spectral parameters of a quadratic bunch of partially symmetrical compact operators in the Hilbert space.

A method is offered for the description of heat transfer (diffusion) processes in fractal systems based on the heat conductivity equation enhanced by an additional variable specifying a scale of the consideration of the fractal.