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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2011 • Question 7

Question

Math 6610 • Analysis of Numerical Methods I Fall 2011 • Question 7
**CFL Condition** a) Explain what we mean by the CFL (Courant-Friedrichs-Lewy) Condition b) Obtain CFL condition for the upwind scheme (explicit) below: \[ u_{i,j+1}=(1-\lambda)u_{i,j}+\lambda u_{i-1,j}, \] where \(i=1,2,\ldots,N+1\) and \(j=0,1,2,\ldots,M-1\) \[ \lambda=\frac{a\Delta t}{h},\qquad \Delta t=T/M, \] and \(a\) is a positive constant.The initial condition is \(u_{i,0}=g_i\)

Raw LaTeX

{CFL Condition}

\partitem{a} Explain what we mean by the CFL (Courant-Friedrichs-Lewy)
Condition

\partitem{b} Obtain CFL condition for the upwind scheme (explicit) below:
\[
  u_{i,j+1}=(1-\lambda)u_{i,j}+\lambda u_{i-1,j},
\]
where \(i=1,2,\ldots,N+1\) and \(j=0,1,2,\ldots,M-1\)
\[
  \lambda=\frac{a\Delta t}{h},\qquad \Delta t=T/M,
\]
and \(a\) is a positive constant.The initial condition is \(u_{i,0}=g_i\)

Topic Tags

Linear Programming and Optimization Zero-Stability and Root Conditions