Draw the computational stencil and
discuss stability for the leapfrog scheme
for the heat equation:
Draw the computational stencil and
discuss stability for the leapfrog scheme
for the convection equation:
What happens in the special case that the Courant number ?
You want to find a central finite difference formula for the
third order derivative . Use central
difference operators to form an approximation involving
the neighboring points j, , ..., .
In particular, find the approximation with the `smallest
stencil' (the smallest value of m). Derive the leading order
truncation error for this approximation.
Discuss consistency and accuracy for the leapfrog scheme
for the heat equation of question 1.
Use operators instead of a Taylor series.
What is your final conclusion about this method?
Discuss consistency and accuracy for the leapfrog scheme
for the convection equation of question 2.
Use operators instead of a Taylor series.
What happens in the special case that the Courant number ?
What is your final conclusion about this method?
Verify accuracy and stability for the Lax-Friedrichs scheme.
Use the operator tables to do both.
Examine the CFL restriction for the Lax-Friedrics scheme.
Compare with the exact analysis of stability and consistency.
Examine the CFL restriction for the backward-time, central-space
scheme for the heat equation.
Verify accuracy and stability for the backward-time, central-space
scheme for the heat equation. Compare with the CFL restriction.