The research of numerical verification methods for nonlinear integral equations with singularity

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740074
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto University
• Principal Investigator: KINOSHITA Takehiko 京都大学, 健康長寿社会の総合医療開発ユニット, 講師 (30546429)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 積分方程式 / 微分方程式 / 有限要素法 / 精度保証付き数値計算

Outline of Final Research Achievements

We have developed the verification methods for existence of a solution of the ordinary differential equation which equivalent to integral equation of a target. We succeeded in improvement of the necessary the verification method of invertibility for linear elliptic operator and its estimates. Moreover, we have developed the method to add a perturbation to the elliptic operator and sequentially estimates inverse operators. However, even this perturbation method couldn't reach the ordinary differential operator with singularity which was a target. Furthermore, the verification method based on shooting method, solving a boundary value problem by reducing it to the solution of an initial value problem, was also tried. We succeeded in development of new verification method of initial value problem necessary to the case.

Free Research Field

数値解析