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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6620 • Analysis of Numerical Methods II

Fall 2023 • Question 3

Question

Math 6620 • Analysis of Numerical Methods II Fall 2023 • Question 3

(Linear Multistep Methods).

  1. Define linear multistep method (give formula). Give definition of the region of absolute stability.
  2. Show that the region of absolute stability for the trapezoidal method is the set of all complex \(h\lambda \) with \(\operatorname {Real}(\lambda ) < 0\).

Raw LaTeX

(Linear Multistep Methods).
\begin{enumerate}

\item
Define linear multistep method (give formula). Give definition of the region
of absolute stability.


\item
Show that the region of absolute stability for the trapezoidal method is the
set of all complex \(h\lambda\) with \(\operatorname{Real}(\lambda) < 0\).

\end{enumerate}

Topic Tags

Absolute Stability and A-Stability Consistency, Stability, and Convergence Linear Multistep Methods Numerical Quadrature