• Journal of Ship and Ocean Technology
• /
• 제6권1호
• /
• pp.34-53
• /
• 2002

Numerical solution of the forward-speed radiation problem for a half-immersed cylinder advancing in regular waves is presented by making use of the improved Green integral equation in the frequency domain. The B-spline higher order panel method is employed stance the potential and its derivative are unknown at the same time. The present numerical solution of the improved Green integral equation by the B-spline higher order Kelvin panel method is shown to be free of irregular frequencies which are present in the Green integral equation using the forward-speed Kelvin-type Green function.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제21권1호
• /
• pp.1-16
• /
• 2017

The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. The purpose of this paper is to characterize higher order operator splitting schemes and propose several higher order methods. Unlike the first and the second order methods, each of the heat and the free-energy evolution operators has at least one backward evaluation in higher order methods. We investigate the effect of negative time steps on a general form of third order schemes and suggest three third order methods for better stability and accuracy. Two fourth order methods are also presented. The traveling wave solution and a spinodal decomposition problem are used to demonstrate numerical properties and the order of convergence of the proposed methods.

• Journal of applied mathematics & informatics
• /
• 제27권1_2호
• /
• pp.205-215
• /
• 2009

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

• Kyungpook Mathematical Journal
• /
• 제61권1호
• /
• pp.1-10
• /
• 2021

This paper is concerned the finite time blow-up of solution for higher-order nonlinear Kirchhoff-type equation with a degenerate term and a source term. By an appropriate Lyapunov inequality, we prove the finite time blow-up of solution for equation (1.1) as a suitable conditions and the initial data satisfying ||Dmu0|| > B-(p+2)/(p-2q), E(0) < E1.

• 전자공학회논문지A
• /
• 제33A권5호
• /
• pp.85-93
• /
• 1996

The far-zone scattered field patterns of a hyperbolic reflector antenna are analyzed by using uniform geometrical theory of diffraction(UTD). The main objective of this paper is to obtain the higher order diffraction contributions which provide the continuity over the shadow boundaries of the first order solution. to obtain the scattered magnetic field characteristics, the scattered field components of the secodn-order diffraction, diffraction-reflection, diffraction-reflection-diffraction terms are added to the result of the previous research. The results of the present research are compared to those of the first order solution and the method of moments. One can observe the improvemtn of the current approach over the first order solution. also, the results of the present method agree very well with those of the moment methods especially in the transition regions near the first order diffraction shadow boundaries.

• East Asian mathematical journal
• /
• 제39권3호
• /
• pp.319-329
• /
• 2023

In this paper, we consider a stochastic higher-order Kirchhoff-type equation with nonlinear damping and source terms. We prove the blow-up of solution for a stochastic higher-order Kirchhoff-type equation with positive probability or explosive in energy sense.

• Journal of applied mathematics & informatics
• /
• 제24권1_2호
• /
• pp.231-243
• /
• 2007

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearity f in the equation depends on all lower derivatives, and the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• 대한수학회지
• /
• 제45권2호
• /
• pp.405-423
• /
• 2008

By using critical point theorem, we study a higher order difference system, and obtain some new sufficient conditions ensuring the existence of periodic solutions for such a system.

• Kyungpook Mathematical Journal
• /
• 제47권4호
• /
• pp.569-578
• /
• 2007

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.

• Journal of applied mathematics & informatics
• /
• 제40권5_6호
• /
• pp.1117-1128
• /
• 2022

We find several q-differential equations of higher order that has q-tangent polynomials as the solution and obtain its associated symmetric properties.