Math 6610 • Analysis of Numerical Methods I

{Upwind Scheme}

Consider the advection equation
\[
  u_t+5u_x=0,\qquad x_L<x<x_R,\qquad 0<t\le T,
\]
where \(u(x,0)=g(x)\), and \(u(x_L,t)=u_L(t)\) for \(t>0\).

\textbf{a)} Write the Upwind Scheme for this problem.

\textbf{b)} What is the local truncation error of the Upwind Scheme?

\textbf{c)} What is the stencil of the scheme? What is the CFL condition for this
method?

\textbf{d)} Investigate the stability of the method using Von Neumann Stability
Analysis.