MA584 - Numerical Solution of Partial Differential Equations--Finite Difference Methods

Hours: T, TH 4:30PM - 5:45PM, HA 325.

Instructor:

Dr. Alina Chertock
Office: HA 212
Phone: 515-3200
Office hours: T, TH 2:00PM - 3:00PM (or by appointment)
E-mail: chertock@math.ncsu.edu

Prerequisites: 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.

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

Other references:
• 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, SIAM.
• 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.

Course Objectives: 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.

Syllabus:

• 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.

Homework: There will be a number of homework assignments for this class. Some of the problems will involve programming and you can use any computer language you like. No late homework will be accepted.

Homework Assignments

Final project: due on December 16, 2008, 11:00AM.

Final Projects

Grading: Homework - 70%, final project - 30%.

Grading Scale: 86%-100%: A, 71%-85%: B, 61%-70%: C, 55%-60%: D, less than 55%: F   (+ and - will also be used.)

Notifications:

• Students will 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 evaluations:

• Schedule: Online class evaluations will be available for students to complete during the last week of class (8:00AM November 21 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: classeval@ncsu.edu
• More information about ClassEval: http://www2.acs.ncsu.edu/UPA/classeval/

Policy on Attendance, Excused Absences, Missed Work:

NCSU policy, including what constitutes an 'Excused Absence,' is at NCSU policy, including that constitutes an 'Excused Absence,' is at this link.

Academic Integrity Statement:

Students are required to follow NCSU policy available at www.ncsu.edu/provost/academic_regulations/integrity/reg.htm. "Academic dishonesty is the giving, taking, or presenting of information or material by a student that unethically or fraudulently aids oneself or another on any work which is to be considered in the determination of a grade or the completion of academic requirements or the enhancement of that student's record or academic career." (NCSU Code of Student Conduct)

The Student Affairs web site has more information (http://www.ncsu.edu/student_affairs/osc/AIpage/acaintegrity.html ).

Utilization implication of the Honor Pledge:

"I have neither given nor received unauthorized aid on this test or assignment."

Expectations concerning honesty in the completion of test and assignments:

This has been outlined above

Students with Disabilities:

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 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.

Further Information:

NCSU Academic Regulations can be found at www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_policies/