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Article type: Cover
2003 Volume 13 Issue 2 Pages
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Article type: Cover
2003 Volume 13 Issue 2 Pages
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Article type: Appendix
2003 Volume 13 Issue 2 Pages
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[in Japanese]
Article type: Article
2003 Volume 13 Issue 2 Pages
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Published: June 25, 2003
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Isao Kimura, Katsuhiro Sakai
Article type: Article
2003 Volume 13 Issue 2 Pages
139-157
Published: June 25, 2003
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We discuss a numerical scheme with monotonicity preserving properties without additionally introducing artificial diffusions for advection-diffusion equations. This paper proposes "Finite Variable Difference Method (FVDM)", in which the convection term is discretized by using locally optimized numerical fluxes so that the resulting difference equation may satisfy a locally exact solution of steady advection-diffusion equations. The present scheme ensures the monotnicity up to the cell Reynolds number Rm ≒ 3.4 in keeping the second-order accuracy, while the conventional central scheme and the QUICK scheme up to Rm = 2 and Rm = 8/3, respectively. For Rm > 3.4, though the present scheme has the first-order accuracy, the lowest order of its truncation error can be finite but arbitrary small. Numerical experiments show solutions with good quality.
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Eiji Nunohiro, Sugayasu Hirano
Article type: Article
2003 Volume 13 Issue 2 Pages
159-179
Published: June 25, 2003
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When solving 4th order equation by floating decimal point operation, there is Ferrari method famous as a solution method of 4th order equation. In this paper, we apply Brown method that transform 4th order equation into the product of two 2nd order equations directly to floating point operation and propose the effective computation method. And from the relation of coefficient and solution of 4th order equation, we express coefficients and all numerical values in the middle calculation with four solutions, and by analyzing the information on the solutions contained in those coefficients, we show the validity of the Brown method.
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Takayuki Shiina
Article type: Article
2003 Volume 13 Issue 2 Pages
181-190
Published: June 25, 2003
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The unit commitment problem is an important problem for electric power utilities. The unit commitment problem is to determine the schedule of power generating units and the generating level of each unit. The decisions are which units to commit at each time period and at what level to generate power meeting the electricity demand. In this paper we propose a new stochastic programming programming model in which on/off scheduling of generators is made before the value of random demand is known. The solution approach is based on the Lagrangian relaxation method and dynamic programming.
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Yasuaki Hiraoka, Toshiyuki Ogawa, Konstantin Mischaikow
Article type: Article
2003 Volume 13 Issue 2 Pages
191-211
Published: June 25, 2003
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This paper presents a numerical verification method for global bifurcation branches of the stationary solutions to dissipative partial differential equations. The key idea is combining verification method based on the Conley Index Theory with a branch chasing algorithm. In this paper, the verification algorithm is described in detail by taking the Swift-Hohenberg equation as an example. Some of the rigorous numerical results are also shown.
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Ben T. Nohara
Article type: Article
2003 Volume 13 Issue 2 Pages
213-224
Published: June 25, 2003
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This paper focuses on the envelope surface of directional, nearly monochromatic waves and the governing equation of the envelope surface is reduced. The spectrum of nearly monochromatic waves is almost concentrated on a single frequency. Such waves create the envelope in a one-dimensional system. In a two-dimensional system, the envelope surface instead of the envelope in a one-dimensional system can be considered. Two-dimensional nearly monochromatic waves in the meaning of the frequency create the envelope surface. This is simply expanded to a two-dimensional system from a one-dimensional system. The author expands the frequency-based nearly monochromatic waves to the propagation-direction-based nearly monochromatic waves. We have the new concept of directional, nearly monochromatic waves, whose energy is almost concentrated in a single propagation direction. It is shown that directional, nearly monochromatic waves also create the envelope surface, which is featured by time-invariant in a linear system. However the fact that a non-linear system makes the envelope surface time-variant is presented.
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Takuya OOURA
Article type: Article
2003 Volume 13 Issue 2 Pages
225-230
Published: June 25, 2003
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The double exponential formula is well-known as a powerful numerical quadrature rule. The automatic quadrature routine of the double exponential formula is necessary for the procedure of checking the convergence, but the conventional method of estimating discretization error is too simple to have a reliable estimate. In this paper, we propose a new method which robustly estimates the discretization error quite effectively.
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Kazuto Matsuo, Seigo Arita, Jinhui Chao
Article type: Article
2003 Volume 13 Issue 2 Pages
231-243
Published: June 25, 2003
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This paper is a survey on the state-of-the-art of cryptosystems based on the discrete logarithm over algebraic curves on finite fields. The issue on security of these systems against various attacks are firstly considered. Then fast addition algorithms and efficient point counting algorithms for Jacobian varieties of algebraic curves are discussed. These algorithms, although are necessary for construction of algebraic curve cryptosystems, had not been available until very recently. This paper also surveys the known results and the recent advances of related number theoretic algorithms and new developments in construction of algebraic curve cryptosystems.
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Shigenori Uchiyama
Article type: Article
2003 Volume 13 Issue 2 Pages
245-256
Published: June 25, 2003
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Since the invention of the public-key cryptosystem in the 1970's, some number theoretic problems such as the integer factoring and the discrete logarithm problem in finite fields have received a lot of attention. The number field sieve method is currently known as the asymptotically fastest integer factoring algorithm. It is also known that the number field sieve method can be made use of computing discrete logarithms in finite fields due to Gordon and Schirokauer. Besides, Adleman proposed a function field analogue of the number field sieve method, which is known as the function field sieve, to compute discrete logarithms in finite fields. This paper surveys recent results on these two methods, the number field sieve and the function field sieve, of computing discrete logarithms in finite fields.
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Masanari Kida, Koh-ichi Nagao
Article type: Article
2003 Volume 13 Issue 2 Pages
257-271
Published: June 25, 2003
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This paper is intended for a survey on recent research on the group of rational points on elliptic curves. The first part is devoted for the recent progress on the computation of the group. The second part concerns on the constraction of elliptic curves with high rank Mordell-Weil group.
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Takakazu Satoh
Article type: Article
2003 Volume 13 Issue 2 Pages
273-288
Published: June 25, 2003
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This paper surveys recent advances of algorithms for computing order or elliptic curves over finite fields. Let p be the characteristic of the base field of a given elliptic curve. Following a usual convention, we denote a primo different from p by l. Then, for fields of large characteristic, l-adic method known as the SEA algorithm is efficient. Whereas, p-adic method runs much faster for fields of small characteristic.
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Tetsuya Izu, Yuji Kida
Article type: Article
2003 Volume 13 Issue 2 Pages
289-303
Published: June 25, 2003
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This paper reports recent results of interger factorization from theoretic, algorithmic and experimental points of view. We also give introductions of major factorization algorithms, especially the (general) number field sieve (NFS) method.
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Ken NAKAMULA
Article type: Article
2003 Volume 13 Issue 2 Pages
305-320
Published: June 25, 2003
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In this report, we shall give an illustration of recent research on computational algebraic number theory, mainly related to number fields and elliptic curves. The purpose of the paper is to describe the achievement of this area at present so that to what extent we can theoretically and practically compute on each field. We shall not go in detailed explanation of algorithms.
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Article type: Appendix
2003 Volume 13 Issue 2 Pages
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Article type: Appendix
2003 Volume 13 Issue 2 Pages
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Article type: Cover
2003 Volume 13 Issue 2 Pages
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Article type: Cover
2003 Volume 13 Issue 2 Pages
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