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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2017 • Question 8

Question

Math 6610 • Analysis of Numerical Methods I Fall 2017 • Question 8
**Upwind Scheme** Consider the advection equation \[ u_t-5u_x=0,\qquad x_L0\) **a)** Write the Upwind Scheme for this problem. **b)** What is the stencil of the scheme? What is the CFL condition for this method? **c)** Investigate the stability of the method using Von Neumann Stability Analysis.

Raw LaTeX

{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 \(u(x_R,t)=u_R(t)\) for \(t>0\)

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

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

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

Topic Tags

Absolute Stability and A-Stability Consistency, Stability, and Convergence Linear Programming and Optimization Von Neumann Stability Analysis