In this class finite-difference methods will be discussed for the solution of partial
differential equations. The class will
present theoretical issues like convergence and accuracy of schemes, and it will
give the students thorough experience with the numerical methods through projects in which the methods are implemented for various partial differential equations.
The programming (in the HP workstation lab) will make use of FORTRAN/C (incl. graphics) as well as MATLAB. The latter is particularly useful for rapid prototyping. A brief introduction to MATLAB will be given and sample programs (in FORTRAN and MATLAB) will be provided.
Figure: Sequence of graphs (time increasing upwards) showing the scattering and dispersion of a left-traveling wave pulse (red and black) in a medium with a jump in density (green) and an inhomogeneity in the wavespeed (blue).
The technical topics to be discussed will include:
Classification and Some Properties of PDEs, Difference Approximations of Derivatives, Temporal Errors, Difference Approximations and Initial-Boundary-Value Problems, Two-dimensional Problems.
J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks/Cole, 1989
W.H. Press et al., Numerical Recipes, Cambridge University Press, 1992.
The Student Edition of MATLAB, version 4, User's Guide. Prentice Hall, 1995.
Time and Place: Tu Th, 2.30-4.00 in A110 (computer projection room)
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Phone: 491-8316, e-mail: email@example.com
Syllabus and additional information.