• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.215-222
• /
• 2000

A multigrid algorithm is developed for solving the one- dimensional initial boundary value problem. The numerical solutions of linear and nonlinear Burgers; equation for various initial conditions are studied. The stability conditions are derived by Von -Neumann analysis . Numerical results are presented.

• Structural Engineering and Mechanics
• /
• v.68 no.6
• /
• pp.713-720
• /
• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.15 no.25
• /
• pp.11-14
• /
• 1992

This paper presents a method for establishing an initial value of redundancy optimization problem to maximize system reliability of multiconstraint mixed parallel-series system. The constraints not be linear. This paper proposes a new initial value which is near to optimal solution by considering the relative median rate of the unreliability and amount of consumed resources for each subsystem. To show the efficiency of this model. numerical example and comparison with Narasimhalu is illustrated in chapter 4.

• Kyungpook Mathematical Journal
• /
• v.52 no.2
• /
• pp.167-177
• /
• 2012

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.

• Structural Engineering and Mechanics
• /
• v.22 no.2
• /
• pp.131-150
• /
• 2006

Exact analytical solutions for in-plane static problems of planar curved beams with variable curvatures and variable cross-sections are derived by using the initial value method. The governing equations include the axial extension and shear deformation effects. The fundamental matrix required by the initial value method is obtained analytically. Then, the displacements, slopes and stress resultants are found analytically along the beam axis by using the fundamental matrix. The results are given in analytical forms. In order to show the advantages of the method, some examples are solved and the results are compared with the existing results in the literature. One of the advantages of the proposed method is that the high degree of statically indeterminacy adds no extra difficulty to the solution. For some examples, the deformed shape along the beam axis is determined and plotted and also the slope and stress resultants are given in tables.

• Communications of the Korean Mathematical Society
• /
• v.24 no.4
• /
• pp.605-615
• /
• 2009

In this paper, we develop a reliable algorithm which is called the variation of parameters method for solving sixth-order boundary value problems. The proposed technique is quite efficient and is practically well suited for use in these problems. The suggested iterative scheme finds the solution without any perturbation, discritization, linearization or restrictive assumptions. Moreover, the method is free from the identification of Lagrange multipliers. The fact that the proposed technique solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested technique.

• International journal of advanced smart convergence
• /
• v.2 no.1
• /
• pp.18-20
• /
• 2013

The significance, is to introduce a novel way to employ the improved Runge-Kutta fifth order five stage method, here after called as Modified IRK(5,5) method, for system of second order robot arm problem and variations in angles at the joints in which parameters governing with two degrees of freedom which requires lesser number of function evaluations per time step as compared to the existing ones, in order to save time and spaceAn ultimate aim of this present paper is to solve application problem such as robot arm and initial value problems by applying Runge-Kutta fifth order five stage numerical techniques. The calculated output for robot arm coincides with exact solution which is found to be better, suitable and feasible for solving real time problems.

• Proceedings of the Korean Environmental Sciences Society Conference
• /
• 2003.11a
• /
• pp.27-32
• /
• 2003

Atmospheric and oceanic numerical models are usually initial-value and/or boundary-value problems. Change in either initial or boundary conditions leads to a variation of model solutions. Much of the predictability research has been done on the response of model behavior to an initial value perturbation. Less effort has been made on the response of model behavior to a boundary value perturbation. In this study, we use the latest version of the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM3) to study the model uncertainty to tiny SST errors. The results show the urgency to investigate the second kind predictability problem for the climate models.

• Korean Journal of Mathematics
• /
• v.23 no.4
• /
• pp.521-536
• /
• 2015

We investigate the nonlinear motions of discrete loaded cable with different periodic forcing. We present the numerical evidence of the nonlinear motions of the cable by solving initial value problems and obtaining the motions after a long time. There appeared to be various types of nonlinear oscillations over a wide range of frequencies and amplitudes for the periodic forcing term.

• Journal of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1133-1148
• /
• 2016

In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $${\sum\limits^l_{n=0}}c_n{\partial}^n_tu(x,t)-{\rho}(x){\Delta}_{\omega}u(x,t)=H(x,t)$$, defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.