2009 Fall MATH 226-01
Bulletin Course Description Numerical solution of hyperbolic conservation laws. Conservative difference schemes, modified equation analysis and Fourier analysis, Lax-Wendroff process. Gas dynamics and Riemann problems. Upwind schemes for hyperbolic systems. Nonlinear stability, monotonicity and entropy; TVD, MUSCL, and ENO schemes for scalar laws. Approximate Riemann solvers and schemes for hyperbolic systems. Multidimensional schemes. Adaptive mesh refinement. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title NUMERICAL HYPERBOLIC PDE Department MATH Course Number 2009 Fall 226 Section Number 01 Primary Instructor Trangenstein,John Prerequisites Prerequisite: Mathematics 224, 225, or consent of instructor. Course Homepage www.math.duke.edu/~johnt/math226.html
Synopsis of course content
Numerical solution of linear hyperbolic conservation laws: conservative difference schemes, modified equation analysis and Fourier analysis, Lax equivalence theorem. Numerical solution of linear parabolic partial differential equations:
finite difference methods, consistency, stability, convergence and approach to steady state. Iterative linear algebra: iterative improvement, incomplete factorization, gradient methods, minimum residual methods and multigrid. Finite element methods for steady-state problems.
Textbooks
Trangenstein, Numerical Solution of Hyperbolic Partial Differential Equations, Cambridge U. Press
Assignments
There will be weekly programming assignments.
Exams
None.
Grade to be based on
Programming assignments and presentation of a research project.
