• The Pure and Applied Mathematics
• /
• v.15 no.1
• /
• pp.35-45
• /
• 2008

In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.

• Journal of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.319-330
• /
• 2002

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.272-275
• /
• 1997

When a manipulator makes contact with an object having position uncertainty, performance measures vary considerably with the control law. To achieve the optimal solution for this problem, an unique objective function that weights time and impact force is suggested and is solved with the help of variational calculus. The resulting optimal velocity profile is then modified to define a sliding mode for the impact and force control. The sliding mode control technique is used to achieve the desired performance. Sets of experiments are performed, which show superior performance compared to any existing controller.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.41-50
• /
• 2002

We provide local and semilocal theorems for the convergence of Newton-like methods to a locally unique solution of an equation in a Banach space. The analytic property of the operator involved replaces the usual domain condition for Newton-like methods. In the case of the local results we show that the radius of convergence can be enlarged. A numerical example is given to justify our claim . This observation is important and finds applications in steplength selection in predictor-corrector continuation procedures.

• Journal of the Korean Mathematical Society
• /
• v.37 no.6
• /
• pp.1031-1042
• /
• 2000

The equations prescribed in Ω⊂R(sup)n are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than n) from closure Ω. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1039-1046
• /
• 1996

In the theory of partial differential equations with given initial values and boundary values one usually investigates to examine the well-posedness, that is, the unique existence of the solution as well as its continuous dependence on the data. This theory is strong enough for us to determine the situation anywhere and anytime provided that the initial data are actually given. However, in many cases the data are not completely known for us. Then in those situations arise the new problem to determine the unknown initial data by taking other conditions for the solutions.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.103-117
• /
• 2016

Abstract. In this paper, we study a modified stochastic predator-prey system with general ratio-dependent functional response. We prove that the system has a unique positive solution for given positive initial value. Then we investigate the persistence and extinction of this stochastic system. At the end, we give some numerical simulations, which support our theoretical conclusions well.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.829-836
• /
• 2005

In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.865-880
• /
• 2015

We present new sufficient convergence criteria for the convergence of the secant-method to a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence criteria can always be weaker than the corresponding ones in earlier studies. Numerical examples are also provided in this study to solve equations in cases not possible before.

• Journal of Astronomy and Space Sciences
• /
• v.11 no.2
• /
• pp.273-280
• /
• 1994

A linear method for determining three-dimensional motion of a rigid object is presented. In this method, two three-dimensional line correspondences are used. By using three-dimensional information of the features and observing that the rotation is unique regardless of the translation vector, the two components of motion parameters (rotation and translation) are computed separately. Also in this paper, the solution is given without a scale factor which is necessary in other methods that use only the two-dimensional projective constraints.