MA7007: NUMERICAL SOLUTION OF DEs I, Fall 2017

Instructor: Prof. Suh-Yuh Yang (楊肅煜)

• Office: M315, Hong-Jing Hall 

• Phone: 03-4227151 ext. 65130

• E-mail address: syyang@math.ncu.edu.tw

• Homepage: http://www.math.ncu.edu.tw/~syyang/

Office Hours: Tuesday 10:00~11:50 am or by appointment      

Prerequisites: Numerical analysis and some knowledge of a high-level programming language Fortran/C/C++, or software package Matlab: http://matlab.math.ncu.edu.tw/

Textbook: Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady State and Time Dependent Problems, SIAM, Philadelphia, July, 2007

                    Here is the errata page of the book!

References:

• Arieh Iserles, A First Course in the Numerical Analysis of Differential Equations, Second Edition, Cambridge University Press, Cambridge, 2009.

• Hans-Gorg Roos, Martin Stynes, and Lutz Tobiska, Robust Numerical Methods for Singularly Perturbed Differential Equations, Second Edition, Springer-Verlag, Berlin, 2008.

Course Objective: An understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another and their practical implications

General Information: The course will cover the following topics

• Part I: Boundary Value Problems and Iterative Methods
  - Finite difference approximations
  - Steady states and boundary value problems
  - Elliptic equations
  - Iterative methods for sparse linear systems*

• Part II: Initial Value Problems
  - The initial value problem for ODEs
  - Zero-stability and convergence for initial value problems*
  - Absolute stability for ODEs*
  - Stiff ODEs
  - Diffusion equations and parabolic problems
  - Advection equations and hyperbolic systems

Assignments:

• Approximately every two weeks, will consist of theoretical problems or computer projects.

• The students are encouraged to discuss homework with other classmates. However, each student needs to turn in her or his own solution set as well as computer codes. Direct copying is absolutely not allowed.