Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2010 • Question 9

Question

Math 6420 • PDE Spring 2010 • Question 9

Use the \(z\)-transform to solve the system of equations \[ \frac {du_n}{dt}=\frac {1}{h^2}\left (u_{n+1}-2u_n+u_{n-1}\right ), \qquad -\infty <n<\infty \] with \(u_n(t=0)=\sin \frac {2\pi n}{k}\), with \(k\) an integer.

Raw LaTeX

Use the \(z\)-transform to solve the system of equations
\[
  \frac{du_n}{dt}=\frac{1}{h^2}\left(u_{n+1}-2u_n+u_{n-1}\right),
  \qquad -\infty<n<\infty
\]
with \(u_n(t=0)=\sin\frac{2\pi n}{k}\), with \(k\) an integer.

Topic Tags

Fourier Transform and Sampling Theory Heat Equation and Parabolic Equations Linear Programming and Optimization Sobolev Spaces and Energy Estimates