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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6620 • Analysis of Numerical Methods II

Fall 2023 • Question 2

Question

Math 6620 • Analysis of Numerical Methods II Fall 2023 • Question 2

(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).
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.

Topic Tags

Linear Multistep Methods Numerical Differentiation and Finite Difference Operators Numerical Quadrature