MA584 - Numerical Solution of Partial Differential Equations--Finite Difference Methods
Dr. Alina Chertock
Web Page: http://www4.ncsu.edu/~acherto
T 10:30AM - 11:30AM and H 3:00PM - 4:00PM (or by appointment)
Tuesdays and Thursdays
4:30PM - 5:45PM
To access your courses and project spaces, use WolfWare:
The aim of the course is to provide an introduction to numerical methods for solving partial differential equations of elliptic, parabolic and
hyperbolic type. The course will focus on the derivation of methods, on their accuracy, stability and convergence properties, as well as on
practical aspects of their efficient implementation. This course should be very useful for students in applied and computational mathematics,
and in any area of scientific computing and engineering.
- Fundamentals of finite difference methods.
- Consistency, stability, convergence, and error estimates for finite difference methods.
- Steady-state and boundary-value problems.
- Elliptic PDE's.
- Initial-value problems for ODE's.
- Diffusion equations and parabolic problems.
- Advection equations and hyperbolic systems.
- Mixed PDE's.
Requisites and Restrictions
Calculus I-III, some background in linear algebra, numerical analysis, and ordinary and partial differential equations. Some programming
experience (Matlab, Fortran, C, C++, ...). It is possible to participate in this class without part of the recommended background but this
will require you to do a lot of extra reading. Students from all scientific and engineering departments are welcome.
Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems
by Randall J. LeVeque,
This textbook is required.
- I expect you to read sections of the textbook around the time of lectures and attempt homework from those sections. The textbook has
additional examples and discussion that you will find helpful. Some test questions may resemble examples from the textbook.
- U.M. Ascher, Numerical Methods for Evolutionary Differential Equations, SIAM.
- U.M. Ascher and L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations,
- K.W. Morton, D.F Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press.
- J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations , Chapman & Hall.
Homework and Projects
- Homework will be assigned and collected regularly, and will be posted (with deadlines) under "Homework Assignments" on the course website.
The homework should be handed in at the beginning of class on the due date. If you cannot make it to class, please make sure to get me the homework on time.
- Selected problems will be graded in detail. No late homework will be accepted and/or graded.
- You are encouraged to discuss homework with other students, but you must write up the solution in your own words
based on your own understanding. Any marked similarity in form or notation between submissions with different authors will be regarded as evidence of academic dishonesty so protect your work.
- Some of the problems will involve programming and you can use any computer language you like.
- You are encouraged to prepare homework solutions in LaTeX. While preparing your homework solution:
- Make sure all solutions are turned in in order, pages are stapled, with sufficient margins so I can write comments.
- Write out the statement of each problem before writing the solution.
- Write problem solutions in paragraph format, not just as a sequence of equations.
- A number of suggested projects will be posted on this webpage.
- You may either chose one of the suggested projects or a project of your own.
- Before start working on the project, you will need to discuss details of the project (including specific
numerical experiments you will conduct) with the instructor.
Tests and Exams
There will be a final project.
- Final project: due on December 13, 2013, 4:00PM.
- Missed tests/exams:
- There will be NO makeup tests/exams. If you have any conflicts with the assigned dates of the tests please contact me by email up to one
week before the exam.
- If you miss a test without a valid excuse, a zero will be averaged into your grade.
- If you are forced to miss a test, an excuse from a doctor or other appropriate authorities must be presented.
- If the excuse is accepted, your other course work will be adjusted so that you will not be penalized.
Homework - 60%, final project - 40%.
This Course uses the Following (Non-Standard) Letter Grading Scale: 86≤A≤100, 71≤B≤85, 61≤C≤70, 55≤D≤60,
F≤55 (+ and - will also be used).
- I do not curve grades. It is theoretically possible for everyone in the class to get an A (or an F). Your performance depends
only on how you do, not on how everyone else in the class does. It is therefore in your best interests to help your classmates, while keeping
the academic integrity policy in mind.
- All questions about grading should be asked (via a written statement) within a week after a graded
assignment/test is returned. Do not alter the original work!
Requirements for Auditors (AU): Information about and requirements for auditing a course can be found at
Policies on Incomplete Grades: If an extended deadline is not authorized by the Graduate School, an unfinished incomplete grade will automatically change to an F after
either (a) the end of the next regular semester in which the student is enrolled (not including summer sessions), or (b) by the end of 12
months if the student is not enrolled, whichever is shorter. Incompletes that change to F will count as an attempted course on transcripts.
The burden of fulfilling an incomplete grade is the responsibility of the student. The university policy on incomplete grades is located at
http://policies.ncsu.edu/regulation/reg-02-50-03. Additional information relative to incomplete grades for
graduate students can be found in the Graduate Administrative Handbook in Section 3.18.F at
Attendance: Students are expected to arrive on time, to contribute to group work and class discussions, and to stay until the class ends.
Attendance at all meetings of the class is expected.
Absences: NCSU policy, including what constitutes an 'Excused Absence,' is at
- Please check the course webpage regularly, as it will be continuously updated with announcements, any changes in the schedule, homework
problems, solutions, review sheets, and other additional course materials.
- Students will also be notified in class or via email of announcements associated with this course. The email address registered with the
NCSU online directory will be used for this purpose. It is the student's
responsibility to maintain a valid email address and check the email sent to it.
End-of-semester class evaluation
- Schedule: Online class evaluations will be available for students to complete during the last week of class (8:00AM November 22 through
8:00AM December 8)
- Students will receive an email message directing them to a website where they can login using their Unity ID and complete evaluations.
- All evaluations are confidential; instructors will never know how any one student responded to any question, and students will never know
the ratings for any particular instructors.
- Evaluation website: https://classeval.ncsu.edu
- Student help desk: email@example.com
- More information about ClassEval: http://www2.acs.ncsu.edu/UPA/classeval/
Academic Integrity: Students are required to comply with the university policy on academic integrity found in the Code of Student Conduct at
Academic Honesty: See
http://policies.ncsu.edu/policy/pol-11-35-01 for a detailed explanation of academic honesty.
Honor Pledge: Your signature on any test or assignment indicates "I have neither given nor received unauthorized aid on this test or assignment."
Accommodations for Disabilities
Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations,
student must register with the Disability Services Office (http://www.ncsu.edu/dso) located at 1900
Student Health Center, Campus Box 7509, 919-515-7653. For more information on NC State's policy on working with students with disabilities,
please see the Academic Accommodations for Students with Disabilities Regulation at
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affirms its commitment to maintain a work environment for all employees and an academic environment for all students that is free from all
forms of discrimination. Discrimination based on race, color, religion, creed, sex, national origin, age, disability, veteran status, or
sexual orientation is a violation of state and federal law and/or NC State University policy and will not be tolerated. Harassment of any
person (either in the form of quid pro quo or creation of a hostile environment) based on race, color, religion, creed, sex, national origin,
age, disability, veteran status, or sexual orientation also is a violation of state and federal law and/or NC State University policy and will
not be tolerated. Retaliation against any person who complains about discrimination is also prohibited. NC State's policies and regulations
covering discrimination, harassment, and retaliation may be accessed at
http://www.ncsu.edu/equal_op. Any person who feels that he or she has been the subject of
prohibited discrimination, harassment, or retaliation should contact the Office for Equal Opportunity (OEO) at 919-515-3148.