Lecture 6: =1=Truncation Error, Consistency, and Convergence

Local truncation errorObserve: All methods can be written asw n+1 = Q(hλ)w n .Explicit methods can be written asz n+1 = y n + hΦ(z n , t n , h).This gives a truncation error of:τ n+1 (h) = 1 h [y n+1 − z n+1 ] = 1 h [y n+1 − (y n + hΦ(z n , t n , h))]= 1 h (y n+1 − y n ) − Φ(z n , t n , h)} {{ }} {{ }Depends upon methodAll explicit methods() Truncation Error, Consistency, and Convergence 8 October 2012 30 / 54