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 errorThenτ n+1 (h) = 1 h (y n+1 − y n ) − Φ(z n , t n , h)= 1 ()(y n + hf (t n , y n ) + h2h2 (f t + ff y ) n + O(h 3 )) − y n− Φ(z n , t n , h)= f (t n , y n ) + h 2 (f t + ff y ) n + O(h 2 ) − Φ(z n , t n , h)Euler Forward: Φ(z n , t n , h) = f (t n , y n )Modified Euler: Φ(z n , t n , h) = f (t n , y n ) + h(f t + ff y )() Truncation <strong>Error</strong>, <strong>Consistency</strong>, <strong>and</strong> <strong>Convergence</strong> 8 October 2012 32 / 54
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