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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2011 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Fall 2011 • Question 6
**Linear Multistep Methods** a) Define the linear multistep method (give formula). Explain what we mean by its region of absolute stability. b) 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}

\partitem{a} Define the linear multistep method (give formula). Explain what we
mean by its region of absolute stability.

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

Topic Tags

Absolute Stability and A-Stability Consistency, Stability, and Convergence Linear Multistep Methods Linear Programming and Optimization