Math 686, Numerical Solution of Differential Equations (Spring 2020)

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: Due: Tuesday, May 19, 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 (Tentative Plan: STAY TUNED FOR UPDATES)

1/21: Chapter 1: Euler's Method [Ch. 1 Lecture Notes] Homework 1: 1.1, 1.4, 1.5 (Due: Tuesday, January 28)

1/28: Chapter 2: Multistep Methods [Ch. 2 Lecture Notes] [Homework 2] (Due: Tuesday, February 4)

2/4: Chapter 3: Gaussian Quadrature & Runge-Kutta Methods [Ch. 3 Lecture Notes (Quadrature)] [Homework 3] (Due:Tuesday, February 11)

2/11: Chapter 3: Gaussian Quadrature & Runge-Kutta Methods [Ch. 3 Lecture Notes (Runge-Kutta)] [Homework 4] (Due: Tuesday, February 18)

2/18: Chapter 3: Runge-Kutta Methods, Chapter 4: Stiff Equations [Ch. 4 Lecture Notes (Part 1)] [Homework 5] (Due: Tuesday, March 3)

2/25: Chapter 4: Stiff Equations and A-stability [Ch. 4 Lecture Notes (Part 2)]

3/3: Chapter 7: Nonlinear Algebraic Systems [Ch. 7 Lecture Notes] [Homework 6] (Due: Tuesday, March 24)

3/17: Extended Spring Break Stay tuned for details for next week

3/24: Chapter 8: Finite Difference Methods [Ch. 8 Lecture Notes (Part 1)], [Ch. 8 Lecture Notes (Part 2)]

3/31: Chapter 8: Finite Difference Methods continued: Takehome Midterm Exam

4/7: Chapter 9: Finite Element Methods [Ch. 9 Lecture Notes (Part 1)], [Homework 7] (Due: Tuesday, April 14)

4/14: Chapter 9: Finite Element Methods [Ch. 9 Lecture Notes (Part 2)]

4/21: Chapter 10: Spectral Methods

4/28: Chapter 16: Diffusion Equation

5/5: Chapter 16: Diffusion Equation, Chapter 17: Advection Equation

5/19: Final Exam

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