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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2003 • Question 8

Question

Math 6610 • Analysis of Numerical Methods I Fall 2003 • Question 8

Numerical PDEs Consider the Initial-Boundary Value Problem \[ u_t=u_{xx},\qquad x\in [0,1],\qquad t\ge 0, \qquad u\text { given for }x=0,\ x=1,\text { and }t=0. \tag {4} \] Describe the Crank-Nicolson Method, and analyze its local truncation error and stability.

Raw LaTeX

{Numerical PDEs}
Consider the Initial-Boundary Value Problem
\[
  u_t=u_{xx},\qquad x\in[0,1],\qquad t\ge0,
  \qquad u\text{ given for }x=0,\ x=1,\text{ and }t=0. \tag{4}
\]
Describe the Crank-Nicolson Method, and analyze its local truncation error and
stability.

Topic Tags

Absolute Stability and A-Stability Consistency, Stability, and Convergence Linear Programming and Optimization Local Truncation Error and Global Error