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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2012 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Spring 2012 • Question 6

Linear Multistep Methods

Construct an example of:

a) a consistent but not stable (not zero-stable) linear multistep method

b) a stable (zero-stable) but not consistent linear multistep method

What kind of behavior do you expect from the numerical solution produced by the methods in a) and in b)?

Raw LaTeX

{Linear Multistep Methods}

Construct an example of:

\textbf{a)} a consistent but not stable (not zero-stable) linear multistep method

\textbf{b)} a stable (zero-stable) but not consistent linear multistep method

What kind of behavior do you expect from the numerical solution produced by the
methods in a) and in b)?

\vspace{1.3\baselineskip}

Topic Tags

Consistency, Stability, and Convergence Linear Multistep Methods Linear Programming and Optimization Numerical Differentiation and Finite Difference Operators