\documentclass[minion]{homework}
\newcommand{\Reals}{\mathbb{R}}
\doclabel{Math F615: Homework 10}
\docdate{Due: April 13, 2019}
\usepackage{graphicx}
\usepackage{enumerate}
\newcommand{\bfx}{\mathbf{x}}
\newcommand{\bfv}{\mathbf{v}}

\begin{document}

\begin{problems}

\problem  Text, 5.2

\problem  Text, 5.3 

In part c), only answer the question about whether the scheme satisfies the CFL condition.

In part d), you should derive a scheme that \textbf{does} satisfy the CFL condition.

 Now apply both schemes to the wave equation $u_{tt}=u_{xx}$ for $0\le x\le 1$
with initial conditions
\begin{equation}
\begin{aligned}
u(x,0) &= \sin(\pi x)\\
u_t(x,0) &= 0
\end{aligned}
\end{equation}

Solve for $0\le t\le 2$ with $M=60, 100, 600, 1000, 6000$ time steps and with $N=(9/20) M$ space unknowns and generate convergence plots.  What orders
of convergence do you observe?  Can you think of a reason to pick one of these
methods over the other?

\problem  Text, 5.6 a-d

\end{problems}

\end{document}