Lecture 6: =1=Truncation Error, Consistency, and Convergence
Lecture 6: =1=Truncation Error, Consistency, and Convergence
Lecture 6: =1=Truncation Error, Consistency, and Convergence
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Local truncation errorBackward EulerPlugging in11−hλ = 1 + hλ + (hλ)2 + (hλ) 3 + O(h 4 ) into theformula for local truncation error givesτ n+1 (h) = (eλh − Q(λh))y nh= 1 [(1 + hλ + 1 )h2! (hλ)2 + O(h 3 ) ..].. − (1 + hλ + (hλ) 2 + O(h 3 )) y n= 1 (− 1 )h 2 (hλ)2 + O(h 3 ) y n(= − 1 )2 hλ2 + O(h 2 ) y n ⇒ τ n+1 (h) = O(h)() Truncation <strong>Error</strong>, <strong>Consistency</strong>, <strong>and</strong> <strong>Convergence</strong> 8 October 2012 24 / 54