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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Local truncation errorTrapezoidal methodFor the Trapezoidal method, the amplification factor,Q(hλ) = 1 + hλ 21 − hλ 2also has to be exp<strong>and</strong>ed into a Taylor series:when1 + hλ 21 − hλ 2=∣ hλ 2 ∣ < 1.(1 + hλ 2)(1 + hλ 2 + (hλ 2 )2 + ( hλ )2 )3 + O(h 4 )= 1 + hλ + 1 2 (hλ)2 + 1 4 (hλ)3 + O(h 4 )() Truncation <strong>Error</strong>, <strong>Consistency</strong>, <strong>and</strong> <strong>Convergence</strong> 8 October 2012 26 / 54
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