2.6 Computer quiz

1. A Courant-Friedrichs-Levy (CFL) number larger than unity ( ) means that
   
   1. the advection velocity exceeds the characteristic speed of the mesh
   2. explicit and implicit finite difference schemes are always unstable
   3. the numerical solution obtained are necessarily inaccurate

2. Dividing the time step by two to converge an explicit scheme for diffusion, you
   
   1. multiply the mesh interval size by two
   2. keep the mesh interval size fixed
   3. divide the mesh interval size by two
   4. divide the mesh interval size by four

3. A numerical scheme is necessarily unstable if the amplification factor
   
   1. has a real part exceeding unity for one particular wavelength
   2. has an imaginary part exceeding unity for all the wavelengths
   3. has a norm exceeding unity for one particular wavelength
   4. has a real part smaller than zero for short wavelengths

4. Implicit schemes such as Crank-Nicholson
   
   1. are always slower than explicit schemes for the same degree of precision
   2. require the more arithmetic operations per step than explicit schemes in 1D
   3. require the more arithmetic operations per step than explicit schemes in 2D
   4. cannot be used for 2D problems

5. An initial box function
   
   1. is often used when a physical solution is sought for advection problems
   2. should always be avoided to minimize inaccuracies in the physical solution
   3. can make explicit finite difference schemes unstable

6. Compared with other methods, explicit finite difference schemes
   
   1. are easy and robust to execute
   2. are easy to understand and implement in a code
   3. converge rather slowly
   4. should be avoided for wave equations

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