Browsing by Author "Hideaki Kaneko"

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    Efficient numerical technique for solving integral equations
    (2021-03-01) Itthithep Navarasuchitr; Pallop Huabsomboon; Hideaki Kaneko; Mahidol University; Old Dominion University
    In this paper, we apply an numerical technique to solve a solution of linear Volterra Integro- Differential Equations. The numerical technique originally developed by Huabsomboon et al. [P. Huabsomboon, B. Novaprateep, H. Kaneko, On Taylor-series expansion techniques for the second kind integral equations, J. Comput. Appl. Math. 234 (2010) 1446-1472] bases on Taylor-series expansion. Our results shown that the technique is simple and efficient.
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    Error analysis of the p-version discontinuous Galerkin method for heat transfer in built-up structures
    (2007-09-01) Hideaki Kaneko; Kim S. Bey; Peter Z. Daffer; Puntip Toghaw; Old Dominion University; NASA Langley Research Center; Northrup Grumman Space Technology; Mahidol University
    In this paper, we provide an error analysis for the p-version of the discontinuous Galerkin finite element method for a class of heat transfer problems in built-up structures. Also, a general form of the matrix associated with the discretization of time variable using the p-finite element basis functions is established. Many interesting properties of this matrix are obtained. Numerical examples are provided in the last section.
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    Numerical experiments using hierarchical finite element method for nonlinear heat conduction in plates
    (2008-07-15) Hideaki Kaneko; Kim S. Bey; Yongwimon Lenbury; Puntip Toghaw; Old Dominion University; NASA Langley Research Center; Mahidol University
    In this paper, we consider a nonlinear hierarchical finite element method for heat conduction problems over two- or three-dimensional plates. Problems considered are nonlinear because the heat conductivity parameter depends upon the temperature itself. This paper explores a new technique recently proposed by the first author which transforms a nonlinear parabolic problem to a linear problem at the discrete level. We present several numerical examples which demonstrate the efficiency of the current technique. © 2008.
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    On taylor expansion methods for multivariate integral equations of the second kind
    (2012-12-01) Boriboon Novaprateep; Khomsan Neamprem; Hideaki Kaneko; Mahidol University; South Carolina Commission on Higher Education; King Mongkut's University of Technology North Bangkok; Old Dominion University
    A new Taylor series method that the authors originally developed for the solution of one-dimensional integral equations is extended to solve multivariate integral equations. In this paper, the new method is applied to the solution of multivariate Fredholm equations of the second kind. A comparison is given of the new method and the traditional Taylor series method of solving integral equations. The new method is adapted to parallel computation and can therefore be highly efficient on modern computers. The method also gives highly accurate approximations for all derivatives of the solution up to the order of the Taylor series approximation. Numerical examples are given to illustrate the efficiency and accuracy of the method.
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    On Taylor-series expansion methods for the second kind integral equations
    (2010-07-01) Pallop Huabsomboon; Boriboon Novaprateep; Hideaki Kaneko; Mahidol University; Old Dominion University
    In this paper, we comment on the recent papers by Yuhe Ren et al. (1999) [1] and Maleknejad et al. (2006) [7] concerning the use of the Taylor series to approximate a solution of the Fredholm integral equation of the second kind as well as a solution of a system of Fredholm equations. The technique presented in Yuhe Ren et al. (1999) [1] takes advantage of a rapidly decaying convolution kernel k (| s - t |) as | s - t | increases. However, it does not apply to equations having other types of kernels. We present in this paper a more general Taylor expansion method which can be applied to approximate a solution of the Fredholm equation having a smooth kernel. Also, it is shown that when the new method is applied to the Fredholm equation with a rapidly decaying kernel, it provides more accurate results than the method in Yuhe Ren et al. (1999) [1]. We also discuss an application of the new Taylor-series method to a system of Fredholm integral equations of the second kind. © 2010 Elsevier B.V. All rights reserved.
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    Wavelet collocation method and multilevel augmentation method for hammerstein equations
    (2012-05-28) Hideaki Kaneko; Khomsan Neamprem; Boriboon Novaprateep; Old Dominion University; King Mongkut's University of Technology North Bangkok; South Carolina Commission on Higher Education; Mahidol University
    A wavelet collocation method for nonlinear Hammerstein equations is formulated. A sparsity in the Jacobian matrix is obtained which gives rise to a fast algorithm for nonlinear solvers such as the Newton's method and the quasi-Newton method. A fast multilevel augmentation method is developed on a transformed nonlinear equation which gives an additional saving in computational time. © 2012 Society for Industrial and Applied Mathematics.