A new integer-type algorithm for solving higher-order partial differential equations

2016 Fiscal Year Final Research Report

• Project/Area Number: 25600157
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Computational science
• Research Institution: University of Fukui
• Principal Investigator: Sakaguchi Fuminori 福井大学, 学術研究院工学系部門, 准教授 (20205735)
• Co-Investigator(Renkei-kenkyūsha): HAYASHI Masahito 名古屋大学, 大学院多元数理科学研究科, 教授 (40342836)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 微分方程式 / 数値解法 / 整数論 / 連分数 / 超函数

Outline of Final Research Achievements

A new algorithm by means only of four arithmetic operations among integers was proposed and implemented for solving partial differential equations, which are very important in physics, engineering and economics, with a very high accuracy. This is an extension of a similar integer-type algorithm for ordinary differential equations already proposed by the same principal investigator, by means of some ideas based on discrete mathematics.
Though the implementation has not perfectly been completed, several mathematically interesting facts and new prospects were found about this algorithm. For example, it turned out that this numerical algorithm in the field of analysis (differentiation, integration etc) is closely related to the classical number theory.

Free Research Field

応用数学・信号処理