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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2017 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Fall 2017 • Question 6
**Linear Multistep Methods** **a)** Define linear multistep method (give formula). Give definition of the 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 linear multistep method (give formula). Give definition of
the 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