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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2008 • Question 9

Question

Math 6420 • PDE Fall 2008 • Question 9

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

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

Heat Equation and Parabolic Equations Linear Programming and Optimization Sobolev Spaces and Energy Estimates