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Yuki Miura, Shin’ichi Oishi, Kouta Sekine2024 Volume 34 Issue 1 Pages 1-18
Published: 2024
Released on J-STAGE: March 25, 2024
JOURNAL FREE ACCESSAbstract. Existence of a variety of periodic solutions are proved using verified numerical computations for a simultaneous nonlinear delay differential equation modeling an interaction between two adjacent region’s see surface temperature. In this simultaneous equation, one dependent variable describes a see surface temperature near Peru, where El Niño phenomena occurs. The other dependent variable describes a see surface temperature of the adjacent region located easter than the first area, where El Niño phenomena does not occur.
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Munehisa Takahashi, Kouta Sekine, Makoto Mizuguchi2024 Volume 34 Issue 1 Pages 19-32
Published: 2024
Released on J-STAGE: March 25, 2024
JOURNAL FREE ACCESSAbstract. The prior error evaluation of the Galerkin method for the Poisson equation is expressed by the projection, and the constants have been studied to evaluate the convergence and error of the approximate solution. This paper considers error constants for orthogonal projections on finite-dimensional subspaces of the abstract Hilbert space. By proving the converse of the Aubin-Nitsche technique without restricting compactness or the basis, we show that the constants satisfying two inequalities are equal. Next, it is also shown that the best error constant under the compactness assumption is the smallest eigenvalue of the eigenvalue problem.
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