• 전자공학회논문지 IE
• /
• v.44 no.4
• /
• pp.26-29
• /
• 2007

In this paper, we use Lyapunov equations and functions to consider the linear systems with perturbed system matrices. And we consider that what choice of Lyapunov function V would allow the largest perturbation and still guarantee that V is negative definite. We find that this is determined by testing for the existence of solutions to a related quadratic equation with matrix coefficients and unknowns the matrix Riccati equation.

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.281-295
• /
• 2005

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.185-201
• /
• 2014

In this paper, we construct a numerical method to solve singularly perturbed one-dimensional parabolic convection-diffusion problems. We use Euler method with uniform step size for temporal discretization and exponential-spline scheme on spatial uniform mesh of Shishkin type for full discretization. We show that the resulting method is uniformly convergent with respect to diffusion parameter. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. The obtained numerical results show that the method is efficient, stable and reliable for solving convection-diffusion problem accurately even involving diffusion parameter.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.635-648
• /
• 2015

We consider a weakly coupled system of singularly perturbed convection-diffusion equations with discontinuous source term. The diffusion term of each equation is associated with a small positive parameter of different magnitude. Presence of discontinuity and different parameters creates boundary and weak interior layers that overlap and interact. A numerical method is constructed for this problem which involves an appropriate piecewise uniform Shishkin mesh. The numerical approximations are proved to converge to the continuous solutions uniformly with respect to the singular perturbation parameters. Numerical results are presented which illustrates the theoretical results.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.655-664
• /
• 1997

The existence and behavior of a bounded solution for a perturbed nonlinear differential equation of the type $$ (DE) x'(t) + Ax(t) \ni G(x(t)), t \in [0, \infty) $$ is considered. First, we consider the existence of a bounded solution with more simple assumptions using the concept of "the method of lines". Then we devote to study its behavior using recent results of almost non-expansive curve which is developed by Djafari Rouhani.i Rouhani.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.689-706
• /
• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.31-48
• /
• 2010

In this article, we consider singularly perturbed Boundary Value Problems(BVPs) for second order Ordinary Differential Equations (ODEs) with Neumann boundary condition and discontinuous source term. A parameter-uniform error bound for the solution is established using the Streamline-Diffusion Finite Element Method (SDFEM) on a piecewise uniform meshes. We prove that the method is almost second order of convergence in the maximum norm, independently of the perturbation parameter. Further we derive superconvergence results for scaled derivatives of solution of the same problem. Numerical results are provided to substantiate the theoretical results.

• 한국전산유체공학회:학술대회논문집
• /
• 2005.10a
• /
• pp.249-253
• /
• 2005

The turbulence noise generated from blunt trailing-edge is numerically predicted by using the hydrodynamic/acoustic splitting method at the Reynolds number based on thickness of flat plate, $Re_h=1000$, and the freestream Mach number $M_o=0.2$. The turbulent flow field is simulated by incompressible large-eddy simulation and the acoustic field is predicted efficiently with the linearized perturbed compressible equations (LPCE) recently proposed by the authors. The turbulent flow characteristics are validated with the results of the previous experimental study and direct numerical simulation. The acoustic properties predicted from LPCE are compared with the solutions of analytical formulations.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.31 no.9
• /
• pp.814-821
• /
• 2007

A hybrid method is presented for efficient computation of turbulent flow noise at low Mach numbers. In this method, the turbulent flow field is computed by incompressible large eddy simulation (LES), while the acoustic field is computed with the linearized perturbed compressible equations (LPCE) derived in this study. Since LPCE is computed on the rather coarse acoustic grid with the flow variables and source term obtained by the incompressible LES, the computational efficiency of calculation is greatly enhanced. Furthermore, LPCE suppress the instability of perturbed vortical mode and therefore secure consistent and stable acoustic solutions. The proposed LES/LPCE hybrid method is applied to three low Mach number turbulent flow noise problems: i) circular cylinder, ii) isolated flat plate, and iii) interaction between cylinder wake and airfoil. The computed results are closely compared with the experimental measurements.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.19 no.2
• /
• pp.1-6
• /
• 1982

This paper reviews and describes some applications of perturbation theory in the practical analysis of linear systems which involve random parameters. Statistical measures of the system outputs are derived in terms of statistical measures of the system parameters and inputs (i.e., in the way of perturbed linear operator equations). Perturbed state transition matrix is also derived. With simple first-order and second-order linear system models, we compare the accuracy of perturbation results with the exact ones. And the convergence of perturbation series is also investigated.