Lecture 6: =1=Truncation Error, Consistency, and Convergence
Lecture 6: =1=Truncation Error, Consistency, and Convergence
Lecture 6: =1=Truncation Error, Consistency, and Convergence
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Trapezoidal methodTrapezoidal method,w n+1 = w n + h 2 (F (t n, w n ) + F (t n+1 , w n+1 )),Uses the average of Euler forward <strong>and</strong> Euler backward.Is an implicit method.Has amplification factor Q(hλ) = 1+ hλ 21− hλ 2Is stable for h > 0.Has local truncation error of order two.Stability + <strong>Consistency</strong> = <strong>Convergence</strong>. It is a secondorder method..() Truncation <strong>Error</strong>, <strong>Consistency</strong>, <strong>and</strong> <strong>Convergence</strong> 8 October 2012 28 / 54
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