index(1)

# index(1) - What is the molecule How would you compute a...

This preview shows page 1. Sign up to view the full content.

\documentstyle[html,epsf]{article} \setlength{\textwidth}{6.6truein}\setlength{\oddsidemargin}{-.2truein} \setlength{\evensidemargin}{-.2truein}\setlength{\textheight}{9truein} \setlength{\topmargin}{-.4truein}\setlength{\headsep}{.2truein} \setlength{\footskip}{.3truein}\pagestyle{empty} \setlength{\parskip}{\baselineskip} \begin{document} \begin{center} {\bf EGN 5456 \hfill Computational Mechanics \hfill 11/15/99}\\ {\it Closed book \hfill Van Dommelen \hfill 12:40-1:55pm} \end{center} Consider the following scheme for the heat equation: \begin{displaymath} \frac{u_{j}^{n+1}-u_{j}^{n}}{\Delta t} = \frac{u_{j+1}^{n}-u_{j}^{n}-u_{j}^{n+1}+u_{j-1}^{n+1}} {\left(\Delta x\right)^2} \end{displaymath} Analyze this scheme.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: What is the molecule? How would you compute a time plane $n+1$ assuming that time plane $n$ is already known? Under what conditions will this scheme converge for all initial data? What is the accuracy? If you believe in the CFL condition for stability, it implies the scheme can only be stable for $\Delta t << \Delta x$. Does that agree with your results? How would you rate this scheme compared to the standard FTCS for the heat equation? Show all reasoning and intermediate results leading to your answer. \begin{rawhtml} <BR><A HREF="figures/1.gif">Solution page 1.</A> <BR><A HREF="figures/2.gif">Solution page 2.</A> \end{rawhtml} \end{document}...
View Full Document

## This note was uploaded on 07/09/2011 for the course EGN 5456 taught by Professor Dommelen during the Spring '09 term at FSU.

Ask a homework question - tutors are online