• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.253-264
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• 2012

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in the mathematical physics via the (1+1)-dimensional Boussinesq equation by using the following two methods: (i) A further improved ($\frac{G}{G}$) - expansion method, where $G=G({\xi})$ satisfies the auxiliary ordinary differential equation $[G^{\prime}({\xi})]^2=aG^2({\xi})+bG^4({\xi})+cG^6({\xi})$, where ${\xi}=x-Vt$ while $a$, $b$, $c$ and $V$ are constants. (ii) The well known extended tanh-function method. We show that some of the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before which gives more exact solutions than the second method (ii).

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.261-280
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• 2005

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.11-24
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• 2017

Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti-Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.321-331
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• 2024

We consider the numerical treatment of blow-up problems having non-monotonic singular solutions that tend to infinity at some point in the domain. The use of standard numerical methods for solving problems with blow-up solutions can lead to significant errors. The reason being that solutions of such problems have singularities whose positions are unknown in advance. To be able to integrate such non-monotonic blow-up problems, we describe and use a method of non-local transformations. To show the efficiency of the method, we present a comparison of exact and numerical solutions in addition to some comparison with the work of other authors.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.391-398
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• 2024

This article explains how solitons propagate when there is a detuning factor involved. The explanation is based on the nonlinear complex Ginzburg-Landau equation, and we first consider this equation before systematically deriving its solutions using Jacobian elliptic functions. We illustrate that one specific ellipticity modulus is on the verge of occurring. The findings from this study can contribute to the understanding of previous research on the Ginzburg-Landau equation. Additionally, we utilize Jacobi's elliptic functions to define specific solutions, especially when the ellipticity modulus approaches either unity or zero. These solutions correspond to particular periodic wave solitons, which have been previously discussed in the literature.

• Structural Engineering and Mechanics
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• v.11 no.2
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• pp.199-210
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• 2001

Axially compressed circular cylinders repeat symmetry-breaking bifurcation in the postbuckling region. There exist stable equilibria with all symmetry broken in the buckled configuration, and the minimum postbuckling strength is attained at the deep bottom of closely spaced equilibrium branches. The load level corresponding to such postbuckling stable solutions is usually much lower than the initial buckling load and may serve as a strength limit in shell stability design. The primary concern in the present paper is to compute these possible postbuckling stable solutions at the deep bottom of the postbuckling region. Two computational approaches are used for this purpose. One is the application of individual procedures in computational bifurcation theory. Path-tracing, pinpointing bifurcation points and (local) branch-switching are all applied to follow carefully the postbuckling branches with the decreasing load in order to attain the target at the bottom of the postbuckling region. The buckled shell configuration loses its symmetry stepwise after each (local) branch-switching procedure. The other is to introduce the idea of path jumping (namely, generalized global branch-switching) with static imperfection. The static response of the cylinder under two-parameter loading is computed to enable a direct access to postbuckling equilibria from the prebuckling state. In the numerical example of an elastic perfect circular cylinder, stable postbuckling solutions are computed in these two approaches. It is demonstrated that a direct path jump from the undeformed state to postbuckling stable equilibria is possible for an appropriate choice of static perturbations.

• Journal of computational fluids engineering
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• v.21 no.2
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• pp.1-11
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• 2016

Considerable efforts are required to develop a monotone, robust and stable high-order numerical scheme for solving the hyperbolic system. The discontinuous Galerkin(DG) method is a natural choice, but elimination of the spurious oscillations from the high-order solutions demands a new development of proper limiters for the DG method. There are several available limiters for controlling or removing unphysical oscillations from the high-order approximate solution; however, very few studies were directed to analyze the exact role of the limiters in the hyperbolic systems. In this study, the performance of the several well-known limiters is examined by comparing the high-order($p^1$, $p^2$, and $p^3$) approximate solutions with the exact solutions. It is shown that the accuracy of the limiter is in general problem-dependent, although the Hermite WENO limiter and maximum principle limiter perform better than the TVD and generalized moment limiters for most of the test cases. It is also shown that application of the troubled cell indicators may improve the accuracy of the limiters under some specific conditions.

• Journal of computational fluids engineering
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• v.14 no.3
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• pp.86-94
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• 2009

The non-conservative form of momentum equations is often used for some two-phase flow codes instead of a conservative form because of numerical convenience. Another non-conservative form, so called, a semi-conservative form can improve the numerical solution of these codes maintaining the numerical convenience. It is close to the conservative form but still maintains the feature of the non-conservative form. A semi-conservative form of the momentum equations and a non-conservative form of the momentum equations are implemented in CUPID[1] code. The numerical results of the semi-conservative and the non-conservative forms are compared against analytical solutions and the solutions of the FLUENT code that uses the conservative form. The results clearly showed that the semi-conservative form of the momentum equations provides better solutions than the non-conservative form, especially for heterogeneous two-phase flows.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.301-327
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• 2019

The proper orthogonal decomposition (POD) method for time-dependent problems significantly reduces the computational time as it reduces the original problem to the lower dimensional space. Even a higher degree of reduction can be reached if the solution is smooth in space and time. However, if the solution is discontinuous and the discontinuity is parameterized e.g. with time, the POD approximations are not accurate in the reduced space due to the lack of ability to represent the discontinuous solution as a finite linear combination of smooth bases. In this paper, we propose to post-process the sample solutions and re-initialize the POD approximations to deal with discontinuous solutions and provide accurate approximations while the computational time is reduced. For the post-processing, we use the Gegenbauer reconstruction method. Then we regularize the Gegenbauer reconstruction for the construction of POD bases. With the constructed POD bases, we solve the given PDE in the reduced space. For the POD approximation, we re-initialize the POD solution so that the post-processed sample solution is used as the initial condition at each sampling time. As a proof-of-concept, we solve both one-dimensional linear and nonlinear hyperbolic problems. The numerical results show that the proposed method is efficient and accurate.

• Korean Journal of Computational Design and Engineering
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• v.17 no.2
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• pp.79-90
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• 2012

In digital virtual manufacturing simulation, Digital Human widely used to optimal workplace design, enhancing worker safety in the workplace, and improving product quality. However, the case of ergonomics simulation solutions to support digital human modeling, Optimal DHM (Digital Human Model) data needed to develop and perform DHM will collect information related to the production process. So simulation developer has burden of collecting information. In this study, to overcome the limitations of existing solutions, we proposed the ADAGIO(Automated Digital humAn model development for General assembly usIng Ontology) framework. The ADAGIO framework was developed for DHM ontology to support optimal deployment of digital virtual environment and in order to ensure consistency of simulation components that are required for simulation modeling was made of a library.