2.0 Credits,
1, 2 Year,
SprABTue5,6
Akitoshi TAKAYASU
Overview
This lecture introduces a risk verification method by numerical computations of nonlinear mathematical models and a rigorous numerical method to control the risk in numerical computations. Representing phenomena by mathematical models and predicting them by computer simulations are widely used methods for analyzing phenomena, but if the reproducibility of phenomena by mathematical models cannot be verified, unexpected risks are inherent in the analysis of phenomena. In this lecture, as a familiar method of verifying the reliability of mathematical models, each method of simulation using numerical computation is introduced. In particular, we focus on the errors in numerical computation, and discuss "rigorous numerics", which is a numerical computation method that gives correct results by taking account of all errors that occur in numerical computation.
Relation to Degree Program Competences
The general competence of the degree program is related to "1. ability to utilize knowledge," the specialized competence of the degree program is related to "1. basic engineering skills," "2. knowledge of basic theories and related technologies," "3. knowledge of actual problems," and "4. broad perspective and bird's eye view," and the research group competence is related to "1. The research group competence is related to "1. research ability" and "2. expertise.
Course Objectives(Learning Outcomes)
Representation of phenomena around us by mathematical models and their predictions by computer simulations are widely used methods for analyzing phenomena. However, if the reproducibility of the phenomena cannot be verified by the mathematical models, unexpected risks will be inherent in the analysis of the phenomena. Therefore, in this lecture, as a familiar method of verifying the reliability of mathematical models, each method of simulation using numerical computation is introduced. In particular, we pay attention to the errors in numerical computation, and discuss "rigorous numerics", which is a numerical computation method that gives correct results by taking account of all errors that occur in numerical computation.
Textbooks, References,and Supplementary Materials
Textbook
Handouts will be distributed as necessary. Lecture materials will be available on the web.
Reference books
Fundamentals of Numerical Computation with Guaranteed Accuracy, edited by Shin-ichi Oishi, Corona Publishing, 2018, ISBN 978-4-339-02887-4
Numerical Computation with Guaranteed Accuracy," M. Nakao and Y. Watanabe, Science, 2011. 3.
Numerical Computation with Guaranteed Accuracy," by Shin-ichi Oishi, Corona Publishing, 2000.
Others are presented during the lecture.
Other(Behavioral expectations and points to note for students during coursework)
In this lecture, we try to bridge the gap from the basic knowledge to the state-of-the-art research results, so that the students can learn the analysis methods of mathematical models using numerical computation with their hands. We will start from the basic knowledge and sublimate the topics to the most advanced research subjects.