• Journal of applied mathematics & informatics
• /
• 제34권5_6호
• /
• pp.495-508
• /
• 2016

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

• 한국대기환경학회지
• /
• 제23권6호
• /
• pp.708-717
• /
• 2007

In the present study, one of the widely applied equations for gas-solid cyclones, Leith and Licht model, was evaluated based on the 3-D CFD technique. The initial and boundary values of radial position and tangential velocity obtain-ed from the CFD simulation enabled complete calculation of the nonlinear second differential equation. This approach showed about 30% errors between calculations with and without the second order differential term. The calculation by using the simple first order equation presented shorter times to migrate up to the inner wall of the cyclone than by the second order, which theoretically implies higher separation efficiency. Further comparison is now under evaluation in terms of the detailed grade efficiency.

• Advances in nano research
• /
• 제16권5호
• /
• pp.489-500
• /
• 2024

This paper studies the free vibration analysis of the piezo-magneto-thermo-elastic FG nanobeam submerged in a fluid environment. The problem governed by the partial differential equations is determined by refined higher-order State Space Strain Gradient Theory (SSSGT). Hamilton's principle is applied to discretize the differential equation and transform it into a coupled Euler-Lagrange equation. Furthermore, the equations are solved analytically using Navier's solution technique to form stiffness, damping, and mass matrices. Also, the effects of nonlocal ceramic and metal parts over various parameters such as temperature, Magnetic potential and electric voltage on the free vibration are interpreted graphically. A comparison with existing published findings is performed to showcase the precision of the results.

• Journal of applied mathematics & informatics
• /
• 제29권3_4호
• /
• pp.813-829
• /
• 2011

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

• 전산구조공학
• /
• 제6권4호
• /
• pp.83-88
• /
• 1993

시간변수에 대하여 불연속성을 주는 시간불연속 Galerkin 방법을 유한요소법으로 해석하였다. 이 방법은 미분방정식 관점에서 지금까지 요소간에 연속성을 준 일반적 유한요소법과 다르게 임의의 시간요소를 선택, 매 시간단계에서 요소경계에 불연속을 허락함으로서 해의 정확성을 높이고 무조건의 안정을 주는 상미분방정식의 해법인 것이다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제17권4호
• /
• pp.238-266
• /
• 2013

The Interaction Picture (IP) method is a valuable alternative to Split-step methods for solving certain types of partial differential equations such as the nonlinear Schr$\ddot{o}$dinger equation or the Gross-Pitaevskii equation. Although very similar to the Symmetric Split-step (SS) method in its inner computational structure, the IP method results from a change of unknown and therefore do not involve approximation such as the one resulting from the use of a splitting formula. In its standard form the IP method such as the SS method is used in conjunction with the classical 4th order Runge-Kutta (RK) scheme. However it appears to be relevant to look for RK scheme of higher order so as to improve the accuracy of the IP method. In this paper we investigate 5th order Embedded Runge-Kutta schemes suited to be used in conjunction with the IP method and designed to deliver a local error estimation for adaptive step size control.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2005년도 추계학술대회논문집
• /
• pp.608-611
• /
• 2005

In this paper the general equation of motion of damped sandwich beam including arbitrary viscoelastic material layer was derived based on the equation presented by Mead and Markus. The equation of motion of n-layered sandwich beam was represented by (n+3)th order ordinary differential equation. It was verified that the general equation of motion derived in this paper could represent the equations of motions for single-layered, three-layered, five-layered and multi-layered damped beam. Finite element method for the arbitrary-layered damped beam was formulated and programmed using higher order shape functions. Several numerical examples were implemented to show the effects of damped material.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제5권2호
• /
• pp.156-162
• /
• 1998

The main objective of this paper is to study the boundedness of solutions of the differential equation $L_{n} {\chi}＋F(t,{\chi}) = f(t), n {\geq} 2 $(*) Necessary and sufficient conditions for boundedness of all solutions of (*) will be obtainded. The asymptotic behavior of solutions of (*) will also be studied.

• Journal of applied mathematics & informatics
• /
• 제28권1_2호
• /
• pp.383-395
• /
• 2010

In the present paper, we construct the traveling wave solutions involving parameters of nonlinear evolution equations in the mathematical physics via the (3+1)- dimensional potential- YTSF equation, the (3+1)- dimensional generalized shallow water equation, the (3+1)- dimensional Kadomtsev- Petviashvili equation, the (3+1)- dimensional modified KdV-Zakharov- Kuznetsev equation and the (3+1)- dimensional Jimbo-Miwa equation by using a simple method which is called the ($\frac{G'}{G}$)- expansion method, where $G\;=\;G(\xi)$ satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the travelling waves. The travelling wave solutions are expressed by hyperbolic, trigonometric and rational functions.

• Steel and Composite Structures
• /
• 제45권3호
• /
• pp.305-330
• /
• 2022

This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton's principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.