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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2015 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Fall 2015 • Question 6

Linear Multistep Methods

Define linear multistep method (give formula).

a) State necessary and sufficient condition for linear multistep method to be consistent.

b) State root condition for linear multistep method.

c) What can you say about consistency and stability properties of the method: \[ y_{n+1}-3y_n+2y_{n-1}=-h f(y_{n-1})? \]

Raw LaTeX

{Linear Multistep Methods}

Define linear multistep method (give formula).

\textbf{a)} State necessary and sufficient condition for linear multistep method
to be consistent.

\textbf{b)} State root condition for linear multistep method.

\textbf{c)} What can you say about consistency and stability properties of the
method:
\[
  y_{n+1}-3y_n+2y_{n-1}=-h f(y_{n-1})?
\]

Topic Tags

Consistency, Stability, and Convergence Linear Multistep Methods Linear Programming and Optimization Zero-Stability and Root Conditions