Higher Order Numerical Methods and Their Numerical Analysis for Mathematical Models of Taxis Phenomena

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04987
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Yamagata University
• Principal Investigator: FANG Qing 山形大学, 理学部, 教授 (10243544)
• Research Collaborator: ZHANG Xiao-Yu ; WANG Ruyun
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 偏微分方程式 / 数値解法 / 高精度 / 有限差分法 / 数値解析 / 数理モデル

Outline of Final Research Achievements

Nonlinear parabolic partial differential equations are used in mathematical models to describe taxis phenomena arising from physics, chemistry, biology and other fields of natural scences. Since analytic solutions can not be obtained in general, it is an important research theme to get highly accurate numerical solutions which contribute to the development of those fields of natural scences. In this research project, the representative investigates Keller-Segel type problems on unbounded domains and, by successfully obtaining the approximate problems on bounded domains, develops validate methods to solve numerically blow-up solutions. By applying the proposed numerical technique, the representative develops high order numerical methods to elliptic partial differential equations with singular solutions, and Rossby solitary waves excited by the unstable topography in weak shear flow.

Free Research Field

偏微分方程式の数値解析