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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2018 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Spring 2018 • Question 6

Trapezoid rule

For the ODE \(y'=f(t,y)\), the Trapezoid rule is \[ \frac {y_{n+1}-y_n}{\Delta t} = \frac {1}{2}\left (f(t_n,y_n)+f(t_{n+1},y_{n+1})\right ). \] Compute the region of absolute stability for the Trapezoid rule. Is this method \(A\)-stable?

Raw LaTeX

{Trapezoid rule}

For the ODE \(y'=f(t,y)\), the Trapezoid rule is
\[
  \frac{y_{n+1}-y_n}{\Delta t}
  =
  \frac{1}{2}\left(f(t_n,y_n)+f(t_{n+1},y_{n+1})\right).
\]
Compute the region of absolute stability for the Trapezoid rule. Is this method
\(A\)-stable?

Topic Tags

Absolute Stability and A-Stability Consistency, Stability, and Convergence Linear Programming and Optimization Von Neumann Stability Analysis