Study guide: Truncation Error Analysis

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Exact solutions of the finite difference equations

How does the truncation error depend on $\uex$ in finite differences?

One-sided differences: $\uex''\Delta t$ (lowest order)

Centered differences: $\uex'''\Delta t^2$ (lowest order)

Only harmonic and geometric mean involve $\uex'$ or $\uex$

Consequence:

$\uex(t)=ct+d$ will very often give exact solution of the discrete equations ( $R=0$ )!

Ideal for verification

Centered schemes allow quadratic $\uex$

Problem: harmonic and geometric mean (error depends on

$\uex'$ and

$\uex$ )