Truncation error analysis

• Aim (as always): turn difference operators into derivatives + truncation error terms
• One-sided forward/backward differences: error $\Oof{\Delta t}$
• Linearization of $|v^{n+1}|v^{n+1}$ to $|v^n|v^{n+1}$: error $\Oof{\Delta t}$
• All errors are $\Oof{\Delta t}$
• First-order scheme? No!
• "Symmetric" use of the $\Oof{\Delta t}$ building blocks yields in fact a $\Oof{\Delta t^2}$ scheme (!)
• Why? See next slide...