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2022 Fiscal Year Final Research Report

Study on Higher Order Numerical Methods and Dynamical Behavior of Solutions for Mathematical Models

Research Project

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Project/Area Number 19K03613
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionYamagata University

Principal Investigator

Fang Qing  山形大学, 理学部, 教授 (10243544)

Project Period (FY) 2019-04-01 – 2023-03-31
Keywords数理モデル / 周期沈殿現象 / 反応拡散方程式 / 差分スキーム / 数値シミュレーション
Outline of Final Research Achievements

This study considers numerical solutions of the system of nonlinear parabolic partial differential equations called reaction-diffusion equations, which is proposed as a mathematical model of periodic sedimentation phenomena. By constructing and developing a highly accurate finite difference scheme, we have simulated periodic sedimentation phenomena in which belts in one-dimensional space and rings in two-dimensional space are generated. We established the validity of such a mathematical model and contributed to the elucidation of the mechanism of periodic sedimentation phenomena such as the Liesegang pattern.

Free Research Field

応用数学

Academic Significance and Societal Importance of the Research Achievements

無機化学と分析化学の分野において、沈殿溶解平衡は固体とその飽和溶液が共存する系であり、重要な平衡理論の一つである。このような自然現象には、空間1次元において帯状と空間2次元においてリング状が生成するような周期沈殿現象があり、数理モデルとして反応拡散方程式と呼ばれる非線形放物型偏微分方程式が提案されている。本研究の成果は、周期沈殿現象の数理モデの確立とそのメカニズムの解明に十分な意義をもつことになったと思われる。

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Published: 2024-01-30  

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