New Development of Numerical Methods for Partial Differential Equations with Singularities

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540108
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Yamagata University
• Principal Investigator: FANG QING 山形大学, 理学部, 教授 (10243544)
• Research Collaborator: ZHANG Xiao-Yu
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 偏微分方程式 / 初期境界値問題 / 特異性 / 数値解法 / 高精度 / 有限差分法 / 数値解析 / 誤差評価

Outline of Final Research Achievements

Mathematical models in partial differential equations with singularities have been used frequently in studies of natural phenomena and social phenomena. They are important research themes for the development of every fields in engineering and financial engineering and so on. In this research project, the representative proposed a higher-order finite difference scheme for nonlinear two-point bpundary value problems. The representative also made progresses in the study of numerical solutions of initial-boundary value problems of parabolic equations on two dimensional spatial domains. Results of numerical analysis of the higher order are obtained.

Free Research Field

偏微分方程式の数値解析