2007 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 NUM PARTIAL DIFF EQUA I Department MATH Course Number 2007 Fall 226 Section Number 01 Primary Instructor Liu,Jian-Guo Permission required? N Course Homepage www.math.duke.edu/~jliu/math226.html
Prerequisites
Math 224-5, or consent of the instructor.
Synopsis of course content
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.
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.
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