Math 6610 • Analysis of Numerical Methods I

{Upwind Scheme}

Consider the advection equation
\[
  u_t-9u_x=0,\qquad x_L<x<x_R,\qquad 0<t\le T,
\]
where \(u(x,0)=g(x)\), and \(u(x_R,t)=u_R(t)\) for \(t>0\)

\partitem{a} Write the Upwind Scheme for this problem

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

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

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