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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StabilityAmplification factorw n+1 = Q(hλ)w nThe amplification factor for our methods is given by:Forward Euler: Q(hλ) = 1 + hλ, stable for 0 < h < 2|λ| .Backward Euler: Q(hλ) = 11−hλ, stable for 0 < h.Trapezoidal method: Q(hλ) = 1+ h 2 λ1− h λ,stable for 0 < h.2modified Euler: Q(hλ) = 1 + hλ + 1 2 (hλ)2 , stable for0 < h < 2|λ| .() Truncation <strong>Error</strong>, <strong>Consistency</strong>, <strong>and</strong> <strong>Convergence</strong> 8 October 2012 8 / 54
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