Abstract. In this paper, we investigate the symplecticity of a coupled system of the wave equation and the elastic equation as a model for simulations of a string and a bridge of a piano. Because simulations of acoustical phenomena often face difficulties due to long term simulations, numerical schemes with a good energetic behavior are preferable. As such, the symplectic integrators are promising; however, to apply these integrators, the system must be symplectic. In this paper, we prove that the semi-discretized coupled system is certainly symplectic under a natural assumption. We also performed numerical experiments, thereby confirming the theoretical result.

Abstract. The Block product-type iterative methods are efficient methods for solving linear systems with multiple right-hand sides. These methods can solve them simultaneously. However, when the number of right-hand sides is large, the accuracy of the approximate solution generated by these methods may deteriorate. One of the causes is a gap between the recursive residual matrix and the true residual matrix. In this paper, the Block GPBiCG method and the Block BiCGSTAB method are reconstructed for improving the accuracy of the approximate solutions. Moreover, we verify that the proposed methods are often better in accuracy through numerical experiments.

Abstract. In this article we give a survey on quasi-Monte Carlo (QMC) methods, which are a class of high-dimensional numerical integration methods. We start from the classical QMC theory and construction of point sets based on the uniform distribution theory, and then move on to more recent progresses on QMC theory, such as the worst-case error for reproducing kernel Hilbert spaces, construction of special classes of QMC point sets called lattice point sets and digital nets, and their randomization techniques. Finally we show the effectiveness of QMC methods through a series of numerical experiments.

Abstract. The arithmetic operations and functions for Taylor series can be definedeasily, and programming is easy. With these programs, the function defined by arithmetic operations,fundamental functions, conditional statements, etc. can be easily expanded to Taylor series. With these Taylor series, Cauchy principal-Value integrals can be divided into the improper integrals and the regular integrals with singularity on appearance. If the integrals with singularity can be calculated analytically and numerical integration of the regular integrals can be carried out easily, the effective numerical integration methods for these improper integrals will be obtained.