Course title
V04506003
Simulation

 ISHIWATA Tetsuya Click to show questionnaire result at 2018
Course description
In this lecture, you study numerical methods for (nonlinear) ODEs and PDEs and their mathmatical backgrounds. You also practice the programing for the numerical simulations and visualization of the data. By these numerical simulations and visualizations, you understand the behavior of the solutions of some typical mathematical models arinsing in several sciences.
Purpose of class
understand numerical methods for ODEs and PDEs and visualization of the data.
Goals and objectives
  1. understand numerical methods for ODEs and PDEs.
  2. understand mathematical background of the numerical methods
  3. understand the phenomena by numerical simulations and visualization for some examples
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction: mathematical models(ODE and PDE), numrical simution review numerical analysis and differential equations 190minutes
2. numerical methods for ODEs
One step method: Euler method and Runge-Kutta method 		review C programing 190minutes
3. Mathematical background of one step method for ODE:
consistency, convergence 		review C programing 190minutes
4. numrical simulations of ODEs and visualization review C programing and visualization 190minutes
5. nonlinear models(ODE) review differential equation and numrical methods(Euler method, Runge-Kutta method) 190minutes
6. simulations: system of nonlinear ODEs review differential equation and numrical methods(Euler method, Runge-Kutta method) 190minutes
7. Finite difference method(FDM) review finite difference method 190minutes
8. mathematical background of FDM reivew the lecture note 190minutes
9. FD schemes for (nonlinear) models reivew the lecture note 190minutes
10. simulations and visualization: heat equation reivew the lecture note 190minutes
11. simulations and visualization: wave equation reivew the lecture note 190minutes
12. simulations and visualization: convection equation reivew the lecture note 190minutes
13. simulations and visualization: reaction-diffusion(RD) equation reivew the lecture note。 190minutes
14. Group work: simulations and visualization for RD system
Presentation 		reivew the lecture note and prepare the presentation 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 reports Total.
1. 30% 30%
2. 30% 30%
3. 40% 40%
Total. 100% -
Evaluation method and criteria
The reports include the following
　Regular reports
　Group work reports and peer evaluations
　Progress questionnaires for each session

The achievement of students will be evaluated by all reports and submissions. If the score is 60% or more, you can pass.
Textbooks and reference materials
nothing
Prerequisites
differential equation, c programing
Office hours and How to contact professors for questions
  • Thu. 12:35-13:05
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Fri Mar 18 22:31:07 JST 2022