• 대한수학회보
• /
• 제40권2호
• /
• pp.243-251
• /
• 2003

This note Presents sufficient conditions for Lyapunov's stability and instability of a class of nonlinear nonautonomous second-order ordinary differential equations. Such a class includes as particular cases a remarkably large number of differential equations with specific physical applications. Two successive nonlinear transformations are applied to the original differential equation in order to convert it into a more convenient form for stability analysis purposes. The obtained stability / instability conditions depend closely on the parameterization of the original differential equation.

• 대한수학회지
• /
• 제53권1호
• /
• pp.127-146
• /
• 2016

We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1989년도 추계학술대회 논문집 학회본부
• /
• pp.505-508
• /
• 1989

A computer simulation code of UV preionized discharge KrF laser is developed, including time dependent circuit equations, boltzmann equations, and plasma kinetic equations for various atomic and molecular species. Rate constants for electron collision processes are calculated with a boltzmann equations as a function of E/N. In this study, we studied mainly the $KrF^*$ formation process, relaxation process, and the 248nm absorption process as a function of charging voltage.

• 천문학논총
• /
• 제18권1호
• /
• pp.15-20
• /
• 2003

In the earlier papers we analyzed the axisymmetric, nonstationary electrodynamics of the central black hole and a surrounding thin accretion disk in an active galactic nucleus. Based on those papers we analyze the axisymmetric, nonstationary black hole magnetosphere in this paper. We concentrate on deriving the ‘Grad-Shafranov equations’; both in the force-free and non-force-free cases. In the time-independent limit our equations naturally coincide with stationary equations as they should.

• Journal of applied mathematics & informatics
• /
• 제6권3호
• /
• pp.747-756
• /
• 1999

The Newtom method and the quasi-Newton method for solving equations of smooth compositions of semismooth functions are proposed. The Q-superlinear convergence of the Newton method and the Q-linear convergence of the quasi-Newton method are proved. The present methods can be more easily implemeted than previous ones for this class of nonsmooth equations.

• East Asian mathematical journal
• /
• 제34권3호
• /
• pp.265-285
• /
• 2018

The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

• Journal of applied mathematics & informatics
• /
• 제7권3호
• /
• pp.813-831
• /
• 2000

In recent years, the theory of Wiener-Hopf equations has emerged as a novel and innovative technique for developing efficient and powerful numerical methods for solving variational inequalities and complementarity problems. In this paper, we provide an account of some of the fundamental aspects of the Wiener-Hopf equations with major emphasis on the formulation, computational algorithms, various generalizations and their applications. We also suggest some open problems for further research with sufficient information and references.

• Journal of applied mathematics & informatics
• /
• 제32권3_4호
• /
• pp.455-464
• /
• 2014

We establish some new criteria for the oscillation of mth order nonlinear difference equations. We study the case of strongly superlinear and the case of strongly sublinear equations subject to various conditions. We also present a sufficient condition for every solution to be asymptotic at ${\infty}$ to a factorial expression $(t)^{(m-1)}$.

• Journal of applied mathematics & informatics
• /
• 제29권3_4호
• /
• pp.847-858
• /
• 2011

We make use of the simplified Hirota's bilinear method with computer symbolic computation to study a variety of coupled potential KdV (pKdV) equations. Each coupled equation is completely integrable and gives multiple soliton solutions and multiple singular soliton solutions. The phase shifts for all coupled pKdV equations are identical whereas the coefficients of the obtained solitons are not identical. The four coupled pKdV equations are resonance free.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1133-1143
• /
• 2009

In this work, we successfully extended dimensional differential transform method (DTM), by presenting and proving some new theorems, to solve the non-linear matrix differential Riccati equations(first and second kind of Riccati matrix differential equations). This technique provides a sequence of matrix functions which converges to the exact solution of the problem. Examples show that the method is effective.