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Kazuaki Nakamura, Daisuke Takahashi2018 Volume 28 Issue 3 Pages 134-141
Published: 2018
Released on J-STAGE: September 25, 2018
JOURNAL FREE ACCESSAbstract. Some evolution equations constructed from max and min operators are considered. Evolution of maximum and minimum values and of sign of solution is discussed relating to the cellular automaton included by the equation as a special case. Moreover, time-asymptotic behavior of solution is analyzed.
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Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake, Shao-Liang Zhang2018 Volume 28 Issue 3 Pages 142-161
Published: 2018
Released on J-STAGE: September 25, 2018
JOURNAL FREE ACCESSAbstract. The matrix fractional power Aα can be represented as an improper integral for a slowly decaying function over the half infinite interval. Conventional approaches to approximating the integral are to apply Gaussian quadrature after some variable transformations; however, the convergence could be slow for an ill-conditioned matrix or a specific value of α. To avoid such situation, we consider the Double Exponential (DE) formula instead of conventional approaches, propose algorithms with settings of the integration interval, and then we show some numerical results.
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