• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.49-56
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• 2006

The aim of the present work is to obtain the inverse Laplace transform of the product of the factors of the type $s^{-\rho}\prod\limit_{i=1}^{\tau}(s^{li}+{\alpha}_i)^{-{\sigma}i}$, a general class of polynomials an the multivariable H-function. The polynomials and the functions involved in our main formula as well as their arguments are quite general in nature. On account of the general nature of our main findings, the inverse Laplace transform of the product of a large variety of polynomials and numerous simple special functions involving one or more variables can be obtained as simple special cases of our main result. We give here exact references to the results of seven research papers that follow as simple special cases of our main result.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.151.1-151
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• 2001

This paper establishes some integral equalities formulated by zeros located in the convergence region of Laplace transformable function. Using the definition of Laplace transform, it is shown that time-domain integral equalities have to be satisfied by the function, and those can be applied to understanding of the fundamental limitations of the control system represented by the transfer function, which has been Laplace transform. In the unity-feedback control scheme, another integral equality is also derived on the output response of the system with open-loop poles and zeros located in the convergence region.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.401-409
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• 2004

In this paper, we show that C-resolvent of generator can be represented by Laplace transform and establish an exponential formula for C regularized semigroups whose antiderivatives are exponentially bounded.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.165-177
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• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.

• Proceedings of the KIEE Conference
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• 1997.07a
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• pp.309-311
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• 1997

In this paper, it is proposed that a algorithm which is applicable to the transient analysis by combined use of the Laplace transform and the finite element method. The proposed method removes the time terms using the Laplace transform and then solves the associated equation with the finite element method. The solution which is solved at frequency domain is transformed into time domain by use of the Laplace inversion. To verify proposed algorithm, heat conduction problem is analysed and found a good agreement with analytic solution.

• Journal of KSNVE
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• v.7 no.1
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• pp.135-142
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• 1997

This paper presents a digital modeling technique of the distributed system. The basic idea of the proposed technique is to discretize a continuous system with respect to the spatial coordinates using bilinear method. The response of the discretized system is analyzed by Laplace transform and z-transform. The computational results in torsional shaft and Timoshenko beam using the proposed technique are compared with the exact solutions and the results of finite element method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.9-16
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• 1994

In this paper, a boundary integral equation for transient plate bending problem is proposed. Approach, using laplace transform is considered. The boundary integral equations with respect to deflection, normal slope, bending moment effective shear are presented and the effect of corner point is considered.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1376
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• 2019

We investigate the valuation of participating life insurance policies with default risk under a geometric regime-switching jump-diffusion process. We derive explicit formula for the Laplace transform of the price of participating contracts by solving integro-differential system and then price them by inverting Laplace transforms.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.559-565
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• 2005

In this paper, we establish the convergence of semigroups that are strongly continuous on (0, $\infty$). By using Laplace transform theory, we show some properties of semigroups and the convergence result.