We discuss a boundary element approach to the initial boundary value problem of the wave equation. We estimate the discretization error of the boundary intetgral equation and show the unique solvability of the discretized equation. We present some numerical examples which suggest the unconditional stability of the scheme proposed in the present paper.

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In this paper an iterative formula for the simultaneous determination of solutions of a nonlinear equation f(z)=0 is proposed. The Durand-Kerner method which is one of simultaneous iterative methods uses only function values of f(z) and does not require any higher order derivatives of f(z). Whereas it is applicable for only polynomial equations. Our method is based on the rational interpolation of f(z) on several points of approximation without derivatives of f(z) as the Durand-Kerner method. Moreover, it is applicable not only for polynomial equations but also for transcendental equations.

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Applications of the Fourier transform are confined to analyses of stationary signals whose properties do not evolve in time. For the analysis of non-stationary signals whose frequencies vary with time, time-frequency two-dimensional representations must be applied. Those are members of Cohen's class, RID(Reduced Interference Distribution)and Scalogram. In this paper, a unified framework of such representations is proposed. In the newly proposed approach, a smoothing function is introduced to provided to provide a continuous transition between spectrogram and scalograms via wigner distribution. Then comparisons among spectrograms, scalograms, obtained by smoothing function acting on Wigner distribution, and RID were made for both simulated and measured signals. As a result of analyses, it is made clear that a best description of non-stationary signals is given by the RID among them.

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In this paper, we discuss the improvements of the global convergence of Newton-Raphson iterations for non-linear equations Fx=0 by using the form G(x)Fx=0 which we will call the functon-multiplied form. Several Julia set graphics are shown to illustrate the effect of G′(x).Further, the algorithms with directivity and with non-stationary approachs are proposed.

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In this paper Incomplete LU factorization well-suited to the vector processor is proposed by consideration on difference schemes. The distribution of stencils of the present difference scheme differs from that of a stansard 5-point difference scheme for gaining high efficiency. The gridpoints on the horizontal line can be simultaneously updated on the vector processor. The convergence property of the ILU factorization for this variant of difference scheme is explored from the view point of the number of iterations, computing times and accuracy of converged solutions. High efficiency of the proposed method on the vector processor will be shown in a series of numerical experiments.

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A lot of discrete approximation schemes in the mean-square sense were proposed for stochastic differential equations. Numerical experiments for these schemes can be seen in some papers, but the efficiency of scheme with respect to its order has not been revealed. We already proposed another type of error analysis, that is by means of separating it into two parts(deterministic and stochastic). However, we only investigated the deterministic part, not the stochastic part. In this paper we will examine the stochasric part of global error of numericali solutions for stochastic differential equations, assuming that the normal random numbers are realized ideally. An analysis shows that the simulation for the integral ∫ sdW(s) by 1/2hΔW_i should be carried out carefully. Our results are consistent to Newton's.

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It is not possible to apply the conventional mode-superposition technique to a coupled acoustic-structural system. So the authors developed the method of modal frequency response and its sensitivity analysis for a coupled acoustic-structural system. However these were extended to a coupled system based on the conventional method of the structural system. Thus, unless the sufficient number of modes are used the good accuracy is not obtained. In this paper the authors illustrated the sensitivity analysis based on the new model superposition method derived by them. Its efficiency is verified by a simple cabin model of a vehicle and particular improvement of the convergence is discussed in detail.

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The spread of STD(sexually transmitted disease)depends upon the distribution of size of SCG(sexually closed group), which is defined as a group consisting of men and women who are sexually related directly or indirectly. However, we cannot make a direct investigation of the size of SCG's in actual society. Our purpose is to estimate the distribution of the size of SCG. What we can investigate is only the distribution of the numbers of the sexual partners. In this paper we propose an algorithm which estimates size of the cluster(e.g.SCG)formed by the simulation based on only the distribution of numbers of the partners.

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In this paper, we present algorithms for computing seueral kinds of normal forms of square matrices ouer the rational number field. The computation is carried out exactly by a computer algebra system, hence the result is free from any numerical errors. An improued algorithm for computing Jordan Normal Forms without the defect contained in the already-known algorithms was shown in our preuious paper. We extend the algorithm to the computation of Second Natural Normal Forms, Jacobson Normal Forms, and transformation matrices into Jordan Normal Forms. We implement the algorithms on the computer algebra system REDUCE3.3 and compute the normal forms. The result shows the practical efficiency of our algorithms.

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An efficient multi-dimensional FFT algorithm for vector processors has been developed. In the algorithm, the multi-dimensional array to be transformed is converted to a one-dimensional array so that simultaneous vector processes are effectively executed. Afterwards, the one-dimensional array is re-converted to an array with the original dimensions. The computational time is substantially reduced with a highly vectorized computer code. The authors compared the computational time for the present algorithm with that for conventional algorithms for a 3-D FFT on the Cray Y-MP.

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Mhaskar and Saff [6] have recently introduced the important notion of weighted capacity, which is a generalization of classical one. In this onte, using the weighted capacity we will introduce an asymptotic theorem on weighted extremal polynomials. The theorem may be applied to some problems.

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