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4 cards from this section. Quick, good the night before a test.
Explain what truncation error is in finite difference methods.
Think about series expansions and the approximation process.
What does the term 'consistency' mean in the context of numerical methods?
Reflect on how the method should behave as parameters are refined.
What is the main purpose of finite difference methods?
Consider the main applications of these methods in computational fluid dynamics.
True or False: Consistency means that as delta x approaches zero, the finite difference solution becomes the exact PDE solution.
Think about how definitions of mathematical terms relate to convergence.
Given an equation: 1 - m^2 φ_{xx} + φ_{yy} = 0, classify it for m values < 0, = 1, and > 1. Provide the reasoning.
Consider how the coefficients relate to each condition in the discriminant.
Perform a von Neumann stability analysis on the finite difference scheme and derive the stability condition explicitly.
Review the key stability derived during our discussion.
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