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Doshisha University (Private)

Doshisha University (Private)

Phenomena that involve

Phenomena that involve time-dependent probability events are mathematically formulated with stochastic differential equations, which raise many issues that must be solved in their simulation. We are studying topics such as pseudorandom number generators that simulate the standard stochastic process known as the Wiener process on a computer, convergence of the discrete-variable method and its convergence speed, and numerical stability of discrete-variable solutions. Discrete-variable solutions of delay-differential equations Analytic solutions of delay-differential equations that appear in control engineering, population dynamics theory, and other fields present more difficulties than typical differential equations, and discrete approximation solutions are required in simulations. We are studying discrete-variable methods, particularly criteria of their numerical stability, and engaged in research on implementation issues and phenomena modeled by difference-differential equations. Research Contents We are currently studying computational mathematics with a focus on numerical analysis. Numerical analysis is a field of mathematical science that can be defined as "the mathematic theory of designing, analyzing, and evaluating numerical algorithms." In many aspects of science and technology, the process of mathematical modeling is repeated, which involves building a mathematical model for analyzing a certain phenomenon using the power of computers, and obtaining qualitative and quantitative data about these problems from the simulation results to open up new knowledge. Most mathematical models are expressed in terms of differential equations, but it is impossible to directly solve differential equations on a computer, and therefore solutions through discretization or approximation are necessary. Creating new algorithms enables us to solve previously unsolvable problems or solve problems thousands of times faster than before, and for this reason, numerical algorithms are critically important for model simulations. Newton, Euler, and other prominent mathematicians in history have contributed to numerical analysis, and with the widespread use of computers today, many more problems are being challenged. Our research ranges from the foundation of this field to its real applications. Keywords Numerical analysis Ordinary differential equation Mathematical modeling Numerical algorithm Parallel computation

Prof. Seiji SAITO Laboratory of Mathematics for Information Science http://istc.doshisha.ac.jp/course/environment/labo_67.html Main Research Topics Stability of ordinary differential equations/difference equations and price-adjustment equations: Michio Morishima (1977) performed numerical calculation of price-adjustment difference equations for price equilibrium of two commodities in order to estimate the eventual stability. Iterative calculations were performed on the relative price (%) of one commodity, and 25,000 to 30,000 were plotted. (Fig. 1) Fuzzy differential equations/optimization: The curves of solutions for fuzzy differential equations which show ambiguous information are drawn from left to right (Fig. 2). The solution methods for bridge optimal location problems with fuzzy hourly traffic volumes (round numbers) of A, B, C, D, Ln, and Rm will solve variational inequalities (Fig. 3). Chaos/fractal analysis: The wings of the Gumowski-Mira are the focus on research into the nature of chaos and randomness (Fig. 4)

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