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 equationThe nonlinear equation isy ′ = f (y) = 2y − 4y 2 .Notice, this is zero at y = 0 <strong>and</strong> y = 1 2 . If β = 1 2, we want todetermine the maximum step-size, h, for which the scheme isstable. We proceed as followsFirst, we linearize f (y) around y = 1 2 .() Truncation <strong>Error</strong>, <strong>Consistency</strong>, <strong>and</strong> <strong>Convergence</strong> 8 October 2012 48 / 54
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