抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research, Category: Grant-in-Aid for Scientific Research (C), Fund Type: competitive_research_funding, Overall Grant Amount: - (direct: 3500000, indirect: 1050000)
The aim of this study is the development and theoretical analysis of numerical computation method based on the hyperfunction theory. The hyperfunction theory is a theory of generalized functions based on the complex analysis, and describes singularities of functions such as poles, discontinuities and the delta functions. In this study, we aim the applications of the hyperfunction theory to numerical computations, namely, we approach to problems involving singularities which make computation difficult by using analytic functions, which are ultimately smooth functions, from the viewpoint of the hyperfunction theory. To be specific, we develop numerical computation methods for integrations with singularities, etc. and consider problems related to numerical computations based on the hyperfunction theory such as the numerical expressions of hyperfunctions.