Numerical Analysis III (PDE)

AMS-528.1

Fall 2009 Tentative Syllabus

Instructor: Roman Samulyak

Office: Math Tower 1-119

Office Phone: 632-8353

Home Page: http://www.ams.sunysb.edu/~rosamu

Email: rosamu@bnl.gov

Class Hours: 3:50 - 5:10pm TuTh in EARTH&SPACE 177

Office Hours: 11:00 - 12:00 am  TuTh or by appointment in Math 1-119

Text book: J. W. Thomas Numerical Partial Differential Equations (I and II) , Spinger-verlag press, ISBN 0-387-97999-9, ISBN 0-387-98346-5.

Attendance: All students are expected to attend all classes and all exams.

ASM 505 Course Description: The main goal of this course is to introduce student to scientific computing and present basic and some advanced numerical techniques for solving partial differential equations that have numerous applications in fundamental and engineering sciences. The emphasis is given on finite difference methods. Finite difference methods are covered for the three major classes of partial differential equations: parabolic, elliptic, and hyperbolic. A brief introduction to finite element, meshless and particle methods for PDE's will also be given. Practical implementation will be discussed as well as the use of important packages of scientific software algorithms.

  • Introduction to finite difference methods for PDE
  • Consistency, convergence and stability, Lax theorem
  • Hyperbolic equations, numerical schemes, stability analysis and CFL condition
  • Parabolic equations, implicit schemes, convection diffusion equations
  • Two dimensional problems, alternate directional implicit (ADI)
  • Numerical dispersion and numerical dissipation, tracking and capturing
  • Conservation Law, Glimm scheme and Godunov scheme, high order schemes, limiter
  • Elliptic equations, iterative methods
  • Introduction to the finite element method
  • Meshless and particle methods for PDE's 

    • ASM 505

    Grading: Homework assignments: 30%
                    Midterm exam: 30%
                    Final Exam: 40%

    Important Note: Students are urged and encouraged to ask questions during and after the class. If you need help, please come to see me during office hours. If you cannot come during office hours, make an appointment and ask questions any other time.

    ASM 505

    Academic Integrity

    Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Any suspected instance of academic dishonesty will be reported to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/

    Americans with Disabilities Act:

    If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.