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5 cards from this section. Quick, good the night before a test.
Define discretization error.
Think about the accuracy of numerical methods.
What causes round-off error?
Consider how computers store numbers.
What type of error is introduced by approximating a PDE with a numerical method?
Think about how both errors originate in numerical methods.
True or False: A method is convergent if its solution approaches the exact solution as grid spacing tends to zero.
Recall the definition of convergence discussed.
Using von Neumann stability analysis, derive the conditions under which a second-order central difference method remains stable in solving the heat equation.
Consider the relationships between grid spacing and time stepping as you set up the equations.
To minimize round-off errors in a computation involving repeated calculations, how can you modify your numerical approach without sacrificing precision?
Reflect on common practices in numerical algorithms regarding error management.
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