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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2020 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Spring 2020 • Question 6

Unstable Multistep Method

Consider the numerical method \[ y_{k+1}=3y_k-2y_{k-1} +\frac {h}{2}\left (f(x_k,y_k)-3f(x_{k-1},y_{k-1})\right ), \qquad k\ge 1 \] Illustrate with an example of a simple initial value problem that the above scheme is unstable.

Raw LaTeX

{Unstable Multistep Method}

\newpage

Consider the numerical method
\[
  y_{k+1}=3y_k-2y_{k-1}
  +\frac{h}{2}\left(f(x_k,y_k)-3f(x_{k-1},y_{k-1})\right),
  \qquad k\ge1
\]
Illustrate with an example of a simple initial value problem that the above
scheme is unstable.

Topic Tags

Linear Multistep Methods Linear Programming and Optimization Numerical Differentiation and Finite Difference Operators Numerical Quadrature