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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ExampleTruncation errorTherefore we have thatz n+1 = y n +hf (t n , y n )+βh 2 (f t +f f y ) n +(βh) 2 (f t +f f y ) n +O(h 3 )We also needy n+1 = y n + h (y n ) ′ + 1 } {{ } 2 h2 (y n ) ′ ′ + O(h 3 )} {{ }=f (t n,y n) =(f t+ff y ) n= y n + hf (t n , y n ) + 1 2 h2 (f t + ff y ) n + O(h 3 ) = y n+1() Truncation <strong>Error</strong>, <strong>Consistency</strong>, <strong>and</strong> <strong>Convergence</strong> 8 October 2012 44 / 54
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