Math 686, Numerical Solution of Differential Equations (Spring 2018)

Tuesday, 7:20pm - 10:00pm, Exploratory Hall, Room 4106


Instructor: Daniel M. Anderson (4411 Exploratory Hall, 703.993.1482, danders1@gmu.edu)
Office Hours: Tuesday/Thursday 3:00PM-4:00PM, and by appointment.

Text: A first course in the numerical analysis of differential equations (Second Edition) by Arieh Iserles.

Prerequisites: Math 214 and Math 446 or 685 including sufficient recall of undergraduate linear algebra, differential equations and computer literacy including familiarity with Matlab.

Course Description: This course will cover the fundamental concepts of numerical methods for differential equations. Students will learn how computational methods are constructed, and how they are used to solve problems arising from the sciences and engineering.

Homework: Homework will include problems that will require the use of Matlab. More specific instructions will follow.

Grading Policy: The course grade will be based on homework (50%), a midterm exam (20%) and the final exam (30%).

Topics Covered/Schedule
Chapter 1 : Euler's Method
Chapter 2 : Multistep Methods
Chapter 3 : Runge-Kutta Methods
Chapter 4 : Stiff Equations
Chapter 6 : Error Control
Chapter 7 : Nonlinear Algebraic Systems
Chapter 8 : Finite Difference Methods
Chapter 9 : Finite Element Methods
Chapter 10 : Spectral Methods
Chapter 16 : Diffusion Equation
Chapter 17 : Advection Equation

FINAL EXAM: Tuesday, May 15, 7:30-10:15pm

Honor System: It is expected that each student in this class will conduct himself or herself within the guidelines of the Honor Code. All academic work should be done with the level of honesty and integrity that this University demands.


Help With Computing:

Set up an account on mason.gmu.edu

Help with Matlab

Very Introductory Matlab Tips

Example Matlab m-file and function m-file
[sam_mfile.m]
[f1.m]


Schedule/Reading/Homework

1/23: Chapter 1: Euler's Method [Ch. 1 Lecture Notes] Homework 1.1, 1.4, 1.5 (Due: Tuesday, January 30)

1/30: Chapter 2: Multistep Methods [Ch. 2 Lecture Notes] [Homework 2] (Due: Tuesday, February 6)

2/6: Chapter 3: Gaussian Quadrature & Runge-Kutta Methods [Ch. 3 Lecture Notes (Quadrature)] [Homework 3] (Due:Tuesday, February 13)

2/13: Chapter 3: Gaussian Quadrature & Runge-Kutta Methods [Ch. 3 Lecture Notes (Runge-Kutta)] [Homework 4] (Due: Tuesday, February 20)

2/20: Chapter 3: Runge-Kutta Methods, Chapter 4: Stiff Equations [Ch. 4 Lecture Notes (Part 1)] [Ch. 4 Lecture Notes (Part 2)] [Ch. 4 Lecture Notes (Part 3)] [Homework 5] (Due: Tuesday, March 6)

2/27: Chapter 4: Stiff Equations [Homework 6] (Due: Tuesday, March 6)

3/6: Chapter 7: Nonlinear Algebraic Systems [Ch. 7 Lecture Notes]

3/13: Spring Break

3/20: Snow Day - takehome midterm distributed - Due 3/27

3/27: Chapter 8: Finite Difference Methods [Ch. 8 Lecture Notes (Part 1)] [Ch. 8 Lecture Notes (Part 2)]

4/3: Chapter 9: Finite Difference Methods - 2D; Finite Element Methods [Homework 8] (Due: Tuesday, April 10)

4/10: Chapter 9: Finite Element Methods [Ch. 9 Lecture Notes (Part 1)] [Ch. 9 Lecture Notes (Part 2)] [Homework 9] (Due: Tuesday, April 17)

4/17: Chapter 9: Finite Element Methods, Chapter 10: Spectral Methods [Ch. 10 Lecture Notes] [Homework 10] (Due: Tuesday, April 24)

4/24: Chapter 10 Spectral Methods, Chapter 16: Diffusion Equation [Ch. 16 Lecture Notes (Part 1)] [Ch. 16 Lecture Notes (Part 2)] [Homework 11] (Due: Tuesday, May 1)

5/1: Chapter 16: Diffusion Equation, Chapter 17: Advection Equation [Ch. 17 Lecture Notes (Part 1)] [Ch. 17 Lecture Notes (Part 2)]

5/8 (??): Chapter 17: Advection Equation, Chapter 10 Spectral Methods

5/15: Final Exam


To Daniel M. Anderson's Homepage