In this paper, we propose a tailored-finite-point method for a type of linear singular perturbation problem in two dimensions. Our finite point method has been tailored to some particular properties of the problem. Therefore, our new method can achieve very high accuracy with very coarse mesh even for very small ε, i.e. the boundary layers and interior layers do not need to be resolved numerica...

If the matrix of a square linear system is nonsingular but has very small singular values, then tiny perturbations of the right-hand side may cause drastic changes in the solution. We show that the probability for this to happen is very close to zero if sufficiently many singular values of the matrix are bounded away from zero.

In this paper, optimal control for stochastic linear quadratic singular neuro Takagi–Sugeno (T-S) fuzzy system with singular cost is obtained using genetic programming(GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The obtained solution in t...

Given a weight of sl(n), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module. Moreover, we completely solve the system in a certain space of power series. The polynomial solutions correspond to the singular vectors in the Verma module. The well-known results of Verma, Bernstein-Gel’f...

The problem of stochastic finite-time guaranteed cost control is investigated for Markovian jumping singular systems with uncertain transition probabilities, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the definitions of stochastic singular finitetime stability, stochastic singular finite-time boundedness, and stochastic singular finite-time guaranteed cost con...

We give a simple example to show that a result on the equivalent singular points of systems of ordinary linear differential equations due to G. D. Birkhoff [3; 5, pp. 252-257] needs amendment. In matrix notation, in which Y, P, etc. denote nXn matrix-valued functions of a complex variable z, this result is as follows. A. Result. Every linear differential system (1) Y'(z) = P(z)Y(z) with a singu...

Solving large scale system of Simultaneous Linear Equations (SLE) has been (and continue to be) a major challenging problem for many real-world engineering and science applications. Solving SLE with singular coefficient matrices arises from various engineering and sciences applications [1]-[6]. In this paper, efficient numerical procedures for finding the generalized (or pseudo) inverse of a ge...

Simulating bubbly flows is a very popular topic in CFD. These bubbly flows are governed by the Navier-Stokes equations. In many popular operator splitting formulations for these equations, solving the linear system coming from the discontinuous Poisson equation takes the most computational time, despite of its elliptic origins. Sometimes these singular linear systems are forced to be invertible...

The aim of this work is to study the dissipative control problem for singular impulsive dynamical systems. We start by introducing the impulse to the singular systems, and give the definition of the dissipation for singular impulsive dynamical systems. Then we discuss the dissipation of singular impulsive dynamical systems, we obtain some sufficient and necessary conditions for dissipation of t...