Solution of a multipoint boundary-value problem for a system of linear ordinary differential equations with holomorphic coefficients

Necessary and sufficient conditions are established for the existence of a unique holomorphic solution of a boundary-value problem for a system of linear ordinary differential equations with holomorphic coefficients and general linear boundary conditions. A procedure for finding this solution is investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 125–128, January, 1990.     

Investigation of a system of linear differential equations with random coefficients

We investigate a system of linear differential equations with random coefficients that depend on a periodic Markov process. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1137–1143, August, 1998.     

Reducibility of a system of linear differential equations with quasiperiodic coefficients

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 12, pp.1669–1680, December, 1989.     

Optimization of a system of linear differential equations with random coefficients

We consider a system of differential equations with controls that are linearly contained in the right-hand sides. We establish a necessary condition for the optimal control that minimizes a quadratic functional. Kiev National Economic University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 556–561, April, 1999.     

Splitting iterative methods for fuzzy system of linear equations

A class of splitting iterative methods is considered for solving fuzzy system of linear equations, which cover Jacobi, Gauss–Seidel, SOR, SSOR, and their block variants proposed by others before. We give a convergence theorem for a regular splitting, where the corresponding iterative methods converge to the strong fuzzy solution for any initial vector and fuzzy right-hand vector. Two schemes of splitting are given to illustrate the theorem. Numerical experiments further show the efficiency of the splitting iterative methods.     

Solution of fuzzy equations with extended operations

Assuming that 1 is any operation defined on a product set X × Y and taking values on a set Z, it can be extended to fuzzy sets by means of Zadeh's extension principle. Given a fuzzy subset C of Z, it is here shown how to solve the equation $\text{A 1 B = C}$ (or $\text{A 1 B ? C}$) when a fuzzy subset A of X (or a fuzzy subset B of Y) is given. The methodology we provide includes, as a special case, the resolution of fuzzy arithmetical operations, i.e. when 1 stands for +, ?, × or ÷, extended to fuzzy numbers (fuzzy subsets of the real line). The paper is illustrated with several examples in fuzzy arithmetic.     

Reducibility of a linear system of differential equations with odd almost periodic coefficients

A theorem on the Kolmogorov reducibility of a system of ordinary differential equations with odd almost periodic coefficients is proved. Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 109–119, July, 1996.     

变系数的分数阶非齐次线性微分方程

主要采用分数阶的幂级数展开的方法,研究α阶和2α阶非齐次线性微分方程解的形式.改进了原有的齐次变系数的分数阶微分方程关于数值解的结论.     

Solution of multivariable fuzzy equations

A method for the solution of multivariable fuzzy equations and inequalities is proposed. The proposed method is an extension of Sanchez' technique for a single fuzzy equation. A numerical example is given.     

Solution to general fuzzy linear system and its necessary and sufficient condition

This paper investigates general fuzzy linear systems of the form Ax = y and general dual fuzzy linear systems of the form Ax + y = Bx + z with A, B matrices of crisp coefficients and x, y fuzzy number vectors. The aim of this paper is twofold. First, by the unique least Euclidean norm solution we solve the systems with non-full rank matrices A, B. Second, we give the new necessary and sufficient condition for a strong fuzzy solution existence. Moreover, some numerical examples are designed.     

Stability of solutions of a system of linear differential equations with periodic stochastic coefficients

Systems of equations for first and second moments are investigated and transformed. Stability of solutions of a first-order linear differential equations is analyzed. Stability of solutions of the stochastic Mathieu equation is investigated and the boundaries of the instability region are determined.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 119–126, 1986.