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.     

Asymptotic Approach to the Solution of a Multicriterion Three-Index Planar Problem of Choice

For a multicriterion three-index planar problem of choice, a polynomial (with respect to the problem dimension) algorithm is proposed and justified that finds the so-called asymptotically ideal solution whose vector estimate tends (in the sense of relative error) to an ideal point (whose coordinates are optimum values of the objective functions of the corresponding one-criterion problems) with increasing the dimension of the problem.     

Haar小波求解线性分数阶微积分方程

分数阶微积分方程的应用逐渐受到广大研究者的重视.论文以Haar小波基函数来逼近线性分数阶微积分方程,通过数值算例的数值解与精确解进行比较,结果表明论文方法是有效的且具有较高的精度.     

Application of a Numerical Increased-Accuracy Method to the Solution of a Heat Transfer Equation

Based on the Hermite formula, a numerical method for solution of a heat transfer equation is described. Expressions are given for computation of the coefficients of the Hermite formula from free parameters. The use of the method is illustrated by an example of solution of a model problem.     

Analytical solution of the linear fractional system of commensurate order

A useful representation of fractional order systems is the state space representation. For the linear fractional systems of commensurate order, the state space representation is defined as for regular integer state space representation with the state vector differentiated to a real order. This paper presents a solution of the linear fractional order systems of commensurate order in the state space. The solution is obtained using a technique based on functions of square matrices and the Cayley-Hamilton theorem. The technique developed for linear systems of integer order is extended to derive analytical solutions of linear fractional systems of commensurate order. The basic ideas and the derived formulations of the technique are presented. Both, homogeneous and inhomogeneous cases with usual input functions are solved. The solution is calculated in the form of a linear combination of suitable fundamental functions. The presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approach.     

Solution of a Matrix Problem on a Mathematical Safe for Locks of the Same Kind. I

A mathematical safe problem is first formulated in a general form. The case of a set of locks that are of the same kind and are arranged in the form of a rectangular matrix is considered. Locks are considered to be of the same kind if their states are specified by numbers from the class of residues to a definite modulus. In the case of a prime modulus, a complete solution is provided. All the results obtained are illustrated by examples.__________Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 155–167, March–April 2005.     

Deriving a discrete approximate solution for a nonlinear dynamic system of two-phase soil media

A discrete approximate generalized solution is derived for a nonlinear differential model of the dynamics of two-phase soil media and its convergence is estimated for the corresponding generalized solution in the space W ₂ ¹ (Ω). Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 69–80, July–August 2009     

Nonclassical Asymptotic Formulas and Approximation with an Arbitrary Order of Accuracy of Eigenvalues of the Sturm-Liouville Problem with Bitsadze-Samarskii Conditions

The Sturm-Liouville problem with Bitsadze-Samarskii conditions is analyzed in the paper. The study is performed in two directions: (i) construction and substantiation of a numerical-analytical method used for deriving eigenfunctions and eigenvalues and (ii) deriving sufficient conditions that are based on the FD-method, that has to provide real eigenvalues, and simplicity and convergence of the generalized nonclassical analytical series.     

Solution Algorithm to a Class of Monetary Rational Equilibrium Macromodels with Optimal Monetary Policy Design

In this paper an extended algorithm using well-known solution methods for monetary models characterized by rational expectations and optimal monetary policy design is given. The extension enables first the use of broad dynamic interdependencies within the structural model of the economy, second stochastic shocks on all endogenous variables and third commitment to a policy displaying no time inconsistency problem. All these points are not entirely new, but are seldom included into an operational solution algorithm. Furthermore a computational improvement concerning the splitting process for the stable and unstable part of the solution is proposed.      

浅谈当前高职院校计算机实验室管理中若干问题的解决方法

该文就当前高职院校计算机实验室管理中存在的若干问题提出了一套切实可行的解决方案,并且对该方案进行了详细的探讨。     

A BSDE approach to a risk-based optimal investment of an insurer

We discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer’s risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. It leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases.     

Interpolation Formulas of the Lagrange Type in a Hilbert Space that are Invariant with Respect to Polynomials

In a Hilbert space, interpolation formulas of the Lagrange type that retain degrees of interpolated polynomials are constructed. The case of a Euclidean space is considered.     

Solvability of nonlocal boundary value problems for ordinary differential equation of higher order with a -Laplacian

Nonlocal boundary value problems at resonance for a higher order nonlinear differential equation with a p-Laplacian are considered in this paper. By using a new continuation theorem, some existence results are obtained for such boundary value problems. An explicit example is also given in this paper to illustrate the main results.