Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2018 • Question 8

Question

Math 6610 • Analysis of Numerical Methods I Spring 2018 • Question 8

Central scheme

Consider the one-dimensional advection equation, \[ u_t=cu_x, \] where \(c\in \mathbb {R}\) is the wavespeed. Use von Neumann stability analysis to determine the values of \(c\) for which the following the central difference, forward Euler scheme is stable: \[ \frac {u_j^{n+1}-u_j^n}{\Delta t} = c\frac {u_{j+1}^{n}-u_{j-1}^{n}}{2h}. \]

Raw LaTeX

{Central scheme}

Consider the one-dimensional advection equation,
\[
  u_t=cu_x,
\]
where \(c\in\R\) is the wavespeed. Use von Neumann stability analysis to determine
the values of \(c\) for which the following the central difference, forward Euler
scheme is stable:
\[
  \frac{u_j^{n+1}-u_j^n}{\Delta t}
  =
  c\frac{u_{j+1}^{n}-u_{j-1}^{n}}{2h}.
\]

Topic Tags

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