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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ExampleNonlinear equationFor stability, we consider the amplification factor with β = 1 2<strong>and</strong> λ = −2 :The method is stable ifQ(hλ) =1 + hλ + β(1 − β)(hλ) 2(1 − 1 2=1−2h + 1 2=1 − 2h + h 2)(−2h) 2|Q(hλ)| = |1 − 2h + h 2 | ≤ 1.() Truncation <strong>Error</strong>, <strong>Consistency</strong>, <strong>and</strong> <strong>Convergence</strong> 8 October 2012 50 / 54
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