Solution Of Problems For Systems Research Articles

Numerical Method for the Solution of Linear Boundary-Value Problems for Integrodifferential Equations Based on Spline Approximations

We propose a numerical method for the solution of linear boundary-value problems for systems of integrodifferential equations. The method is based on the approximation of the integral term by a cubic spline and the reduction of the original problem to a linear boundary-value problem for a system of loaded differential equations. We also propose new algorithms for finding the numerical solutions and a method for the construction of approximate solutions to the approximating boundary-value problems.

Realization of Exact Three-Point Difference Schemes for Nonlinear Boundary-Value Problems on the Semiaxis

New algorithmic realization of exact three-point difference schemes via the three-point difference schemes of high order of accuracy is proposed for the numerical solution of boundary-value problems for systems of nonlinear ordinary differential equations on the semiaxis. We study the existence and uniqueness of the solution of three-point difference schemes and estimate the rate of convergence. The results of numerical experiments are also presented.

Problem of Biomechanical Grippers Identifications Et’s Properties

The specific group grippers are biomechanical grippers, whose shape and construction are analogical to biological model (human hand). These constructions are arranged into category of “intelligent grippers” recently. The analysis of gripping the objects by biomechanical grippers and consequently setting of the model identification of related characteristics and parameter are possible to base on the principles shown. It is possible to secure reliable and safe clamping of manipulated objects in the period of gripper design. This paper gives knowledge from the solution of system problems of manipulated object gripping in the realisation of elements “gripper – manipulated object application requirements” in the period of gripper design.

A system for optimization of the output characteristics of electronic components

A general approach to solution of optimization problems for systems with a large number of degrees of freedom and a set of software objects with open interface are developed and are used for construction of the architecture of a software system for solution of a broad range of optimization problem via the search for the extrema of an objective function with the help of genetic algorithms. Genetic algorithms are used for both optimization of the system itself and selection of the optimum parameters of the genetic algorithm. The software system was evaluated with a large set of problems related to calculation of the topology of surface-acoustic-wave frequency selective filters. The system architecture is built in accordance with the basic principles of the service-oriented architecture.

On solving systems of ordinary differential equations on MIMD-computers

The error of solution of Cauchy problems for systems of ordinary differential equations is estimated in the case where the input data are approximate. It is shown how to prepare a program for computing the right-hand sides of the system automatically and simultaneously. Diagrams are presented to illustrate the efficiency of parallelization.

Primal-dual Newton Methods in Structural Optimization

We consider the numerical solution of optimization problems for systems of partial differential equations with constraints on the state and design variables as they arise in the optimal design of the shape and the topology of continuum mechanical structures. After discretization the resulting nonlinear programming problems are solved by an “all-at-once” approach featuring the numerical solution of the state equations as an integral part of the optimization routine. In particular, we focus on primal-dual Newton methods combined with interior-point techniques for an appropriate handling of the inequality constraints. Special emphasis is given on the efficient solution of the primal-dual system that results from the application of Newton’s method to the Karush–Kuhn–Tucker conditions where we take advantage of the special block structure of the primal-dual Hessian. Applications include structural optimization of microcellular biomorphic ceramics by homogenization modeling, the shape optimization of electrorheological devices, and the topology optimization of high power electromotors.

Polynomial Solution of Predictive Optimal Control Problems For Systems in State-Equation Form

The solution of linear quadratic predictive optimal control problems for systems represented in state-equation form, but using a polynomial systems approach, is considered. A multistep cost-function is used that includes future set-point information. A novel method is introduced for computing the vector of future controls and for solving a simpler optimization problem for the current control.

Algorithmic Foundations of Creation of an Intelligent Software Tool for Investigation and Solution of Cauchy Problems for Systems of Ordinary Differential Equations

Methods are proposed for computer investigation of properties of systems of ordinary differential equations. Based on these methods, algorithms are created for computation of the value of the integration step that provides the stability of a numerical method and obtaining its results with a preassigned accuracy. The components and modes of operation of an intelligent software tool supporting the proposed methods are presented.

On the Convergence of Gradient Methods Used in Solving Singular Optimal Control Problems

We study the convergence and stability of gradient methods for numerical solution of singular optimal control problems for systems with distributed parameters that satisfy a priori inequalities in negative norms.

Aniterative method for the solution of some singularly perturbed cauchy problems

We construct an iterative method for the solution of Cauchy problems for systems of singularly perturbed equations with fast time.

On the relation between algebraic stability andB-convergence for Runge-Kutta methods

This paper is concerned with the numerical solution of stiff initial value problems for systems of ordinary differential equations using Runge-Kutta methods. For these and other methods Frank, Schneid and Ueberhuber [7] introduced the important concept ofB-convergence, i.e. convergence with error bounds only depending on the stepsizes, the smoothness of the exact solution and the so-called one-sided Lipschitz constant β. Spijker [19] proved for the case β<0 thatB-convergence follows from algebraic stability, the well-known criterion for contractivity (cf. [1, 2]). We show that the order ofB-convergence in this case is generally equal to the stage-order, improving by one half the order obtained in [19]. Further it is proved that algebraic stability is not only sufficient but also necessary forB-convergence.

Simulation of MHD processes in high-temperature plasma

The paper analyzes a number of mathematical models and numerical codes developed for the study of magnetohydrodynamic (MHD) processes in high-temperature tokamak plasma. Various approaches are discussed to numerical solution of the nonlinear problems for systems of MHD equations arising in controlled thermonuclear fusion research.

A finite element method for diffusion theory embracing nodal and difference methods

In this exposition of the finite element method for problems of reactor physics and shielding the treatment is restricted to diffusion theory; but the ideas used are also applicable to transport theory, as illustrated in Ackroyd (1981). The principal justification for the finite element method lies in its ability to solve problems for systems with irregular shapes. Many of the papers presented at this seminar deal in detail with such problems. Here attention is focussed on four topics: (i) The principles underlying the finite element method. (ii) An outline of the solution of problems for systems of arbitrary shape. (iii) Generation of finite difference schemes of various degrees of complexity for systems of regular shape. These are methods appropriate for design calculations. (iv) Transformation of finite difference schemes into nodal schemes* to provide solutions rapid and accurate enough to meet the needs of reactor operations. The principles used in the present exposition of the finite element method can be used in three ways: (a) To give a unified treatment of finite element methods. (b) To show that the finite element method includes finite difference and nodal methods as special cases. (c) To provide a posteriori bounds for the global and local errors made by finite element calculations, so that benchmarks can be established additional to those provided by the exact analytical solutions available for simple systems. Here attention is paid mainly to categories (a) and (b). Finite element methods are based usually on one of the following; variational principles, weighted residual

Parallel algorithm for the solution of boundary-value problems for systems of differential equations

Parallel algorithm for the solution of boundary-value problems for systems of differential equations

Optimal control of the temperature field in a rod with a programmed change in the control zone

A. T. Vasilenko, G. P. Golub, Ya. M. Grigorenko, and A. I. Shinkar', "Solution of statics problems of multilayered orthotropic shells of revolutionwith orthotropicvariablethickness layers," Prikl. Mekh., 6, No. 2, 12-17 (1970). A. S. Vo!'mir, Stability of Deformable Systems [in Russian], Nauka, Moscow (1967). S. K. Godunov, "On the numerical solution of boundary-value problems for systems of linear ordinary differential equations," Usp. Mat. Nauk, 16, No. 3, 171-174 (1961). Ya. M. Grigorenko and A. T. Vasilenko, "Nonsymmetric deformation of isotropic and an,sotropic shells of revolution," Prikl. Mekh., ~, No. 3, 19-28 (1968). Ya. M. Grigorenko, G. K. Sudavtsova, and A. I. Shinkar', "Electronic digital computer solution of problems on the nonsymmetric stress state of systems of shells of revolution," Prikl. Mekh., ~, No. ii, 29-35 (1968). Ya. M. Grigorenko, E. I. Bespalova, A. T. Vasilenko, et al., Numerical Solution of Statics Boundary-Value Problems of Orthotropic Layered Shells of Resolution on an Electronic Computer of M-220 Type (Methodological Handbook) [in Russian], Naukova Dumka, Kiev (1971).

Diakoptics—The solution of system problems by tearing

A piecewise procedure called diakoptics is described. An overview of the theory is presented, and a summary of the applications that have been carried out to date in the power industry has been included. This paper is not a mere recapitualtion, but contains a number of new ideas which have not been presented previously. Only relevant mathematics have been included, and derivations or detailed mathematical presentations that appear elsewhere have been referenced. The paper starts with a historical review in which the classic problem through which diakoptics was conceived is presented. The tearing cases considered include torn subdivisions radially attached as well as torn subdivisions not attached. Only the most basic cases are considered for brevity and clarity of presentation.