Establishment of Foundations of Verified Numerical Computations for Nonlinear Systems and Error-free Algorithms in Computational Engineering

Research Project Outline

The purpose of this research is to establish methodologies of designing error-free algorithms for solving various problems in computational engineering. Focus is on the development of efficient algorithms. For this purpose, techniques of verified numerical computations and error-free numerical algorithms will be combined with algorithms in computational engineering. Concretely, foundations of efficient methods of verified numerical computations will be established for finite dimensional nonlinear systems, which appear as fundamental problems of computational engineering. This breakthrough enables us to design efficient error-free algorithms in computational engineering. As a result, it has significant ramifications for various arias of science, engineering and industry.