• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.22 no.4
• /
• pp.289-294
• /
• 2018

In this work, a recently developed semi-analytic technique, so called the residual power series method, is generalized to process higher-dimensional linear and nonlinear partial differential equations. The solutions obtained takes a form of an infinite power series which can, in turn, be expressed in a closed exact form. The results reveal that the proposed generalization is very effective, convenient and simple. This is achieved by handling the (m+1)-dimensional Burgers equation.

• Kyungpook Mathematical Journal
• /
• v.61 no.2
• /
• pp.383-393
• /
• 2021

In this paper, numerical techniques are presented for solving initial value problems of fractional differential equations with variable coefficients. The method is derived by applying a Taylor vector approximation. Moreover, the operational matrix of fractional integration of a Taylor vector is provided in order to transform the continuous equations into a system of algebraic equations. Furthermore, numerical examples demonstrate that this method is applicable and accurate.

• Communications of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.281-298
• /
• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.4
• /
• pp.917-932
• /
• 2024

In this paper, we deal with the Euler-Maruyama (EM) scheme for stochastic differential equations driven by G-Brownian motion (G-SDEs). Under the linear growth and the local Lipschitz conditions, the strong convergence as well as the rate of convergence of the EM numerical solution to the exact solution for G-SDEs are established.

• Structural Engineering and Mechanics
• /
• v.80 no.5
• /
• pp.491-501
• /
• 2021

A difference in subgrade settlement between two rails of a track manifests as lateral differential subgrade settlement. This settlement causes unsteadiness in the motion of trains passing through the corresponding area. To illustrate the effect of lateral differential subgrade settlement on the dynamic response of a vehicle-track coupling system, a three-dimensional vehicle-track-subgrade coupling model was formulated by combining the vehicle-track dynamics theory and the finite element method. The wheel/rail force, car body acceleration, and derailment factor are chosen as evaluation indices of the system dynamic response. The effects of the amplitude and wavelength of lateral differential subgrade settlement as well as the driving speed of the vehicle are analyzed. The study reveals the following: The dynamic responses of the vehicle-track system generally increase linearly with the driving speed when the train passes through a lateral subgrade settlement area. The wheel/rail force acting on a rail with a large settlement exceeds that on a rail with a small settlement. The dynamic responses of the vehicle-track system increase with the amplitude of the lateral differential subgrade settlement. For a 250-km/h train speed, the proposed maximum amplitude for a lateral differential settlement with a wavelength of 20 m is 10 mm. The dynamic responses of the vehicle-track system decrease with an increase in the wavelength of the lateral differential subgrade settlement. To achieve a good operation quality of a train at a 250-km/h driving speed, the wavelength of a lateral differential subgrade settlement with an amplitude of 20 mm should not be less than 15 m. Monitoring lateral differential settlements should be given more emphasis in routine high-speed railway maintenance and repairs.

• Journal of applied mathematics & informatics
• /
• v.30 no.3_4
• /
• pp.555-560
• /
• 2012

In this paper, differential transform method (DTM) is considered to obtain solution to the generalized Fisher's equation. This method is easy to apply and because of high level of accuracy can be used to solve other linear and nonlinear problems. Furthermore, is capable of reducing the size of computational work. In the present work, the generalization of the two-dimensional transform method that is based on generalized Taylor's formula is applied to solve the generalized Fisher equation and numerical example demonstrates the accuracy of the present method.

• Journal of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1209-1229
• /
• 2017

We coupled the so-called Sumudu transform with the homotopy perturbation method (HPM) and the homotopy analysis method (HAM), which are called homotopy perturbation Sumudu transform method (HPSTM) and homotopy analysis Sumudu transform method (HASTM), respectively. Then we show how HPSTM and HASTM are more convenient than HPM and HAM by conducting a comparative analytical study for a system of time fractional nonlinear differential equations. A Maple package is also used to enhance the clarity of the involved numerical simulations.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.17 no.4
• /
• pp.221-237
• /
• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.3
• /
• pp.253-266
• /
• 2019

In this article, a systematic solution based on the sequence of expansion method is planned to solve the time-fractional diffusion equation, time-fractional telegraphic equation and time-fractional wave equation in three dimensions using a current and valid approximate method, namely the ADM, VIM, and the NIM subject to the estimate initial condition. By using these three methods it is likely to find the exact solutions or a nearby approximate solution of fractional partial differential equations. The exactness, efficiency, and convergence of the method are demonstrated through the three numerical examples.

• KIEAE Journal
• /
• v.16 no.6
• /
• pp.13-19
• /
• 2016

Purpose: In this study, we examined outdoor air fraction using historical data of actual Air Handling Unit (AHU) in the existing building during intermediate season and analyzed optimal outdoor air fraction by control types for economizer. Method: Control types for economizer which was used in analysis are No Economizer(NE), Differential Dry-bulb Temperature(DT), Diffrential Enthalpy(DE), Differential Dry-bulb Temperature+Differential Enthalpy(DTDE), and Differential Enthalpy+Differential Dry-bulb Temperature (DEDT). In addition, the system heating and cooling load were analyzed by calculating the outdoor air fraction through existing AHU operating method and control types for economizer. Result: Optimized outdoor air fraction through control types was the lowest in March and distribution over 50% was shown in May. In case of DE control type, outdoor air fraction was the highest of other control types and the value was average 63% in May. System heating load was shown the lowest value in NE, however, system cooling load was shown 1.7 times higher than DT control type and 5 times higher than DE control type. For system heating load, DT and DTDE is similar during intermediate season. However, system cooling load was shown 3 times higher than DE and DEDT. Accordingly, it was found as the method to save cooling energy most efficiently with DE control considering enthalpy of outdoor air and return air in intermediate season.