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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6620 • Analysis of Numerical Methods II

Summer 2024 • Question 2

Question

Math 6620 • Analysis of Numerical Methods II Summer 2024 • Question 2

(20 pts)

  1. (10 pts) Compute the stability/amplification factor for forward Euler to solve \(u' = f(t,u)\), and plot the region of the stability.
  2. (10 pts) Compute the stability/amplification factor for the trapezoidal rule/Crank- Nicolson scheme and use this to show that the scheme is A-stable.

Raw LaTeX

(20 pts)
\begin{enumerate}

\item
(10 pts) Compute the stability/amplification factor for forward Euler to solve \(u' =
f(t,u)\), and plot the region of the stability.


\item
(10 pts) Compute the stability/amplification factor for the trapezoidal rule/Crank-
Nicolson scheme and use this to show that the scheme is A-stable.

\end{enumerate}

Topic Tags

Absolute Stability and A-Stability Consistency, Stability, and Convergence Numerical Quadrature Von Neumann Stability Analysis