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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2000 • Question 9

Question

Math 6420 • PDE Fall 2000 • Question 9

Solve the discretized heat equation \(u_{nt}=\frac {1}{h^2}(u_{n+1}-2u_n+u_{n-1})\) with \(-\infty <n<\infty \) and initial data \(u_n(t=0)=\sin \frac {2\pi n}{k}\) where \(k\) is a fixed integer.

Raw LaTeX

Solve the discretized heat equation
\(u_{nt}=\frac{1}{h^2}(u_{n+1}-2u_n+u_{n-1})\) with \(-\infty<n<\infty\) and initial data
\(u_n(t=0)=\sin\frac{2\pi n}{k}\) where \(k\) is a fixed integer.

Topic Tags

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