Unformatted text preview:  G  = 0 . TR is Astable, but not Lstable. Backward Euler (³rst and secondorder) and TRBDF2 are Lstable. Local Truncation Error ( ± ) du dt = f ( u ) , u ( t = 0) = u The discrete approximation is u n ≈ u ( n Δ t ). The onestep discretized version of the initial value problem ( ± ) can be written as u n +1 = u n + Δ t Φ( u n , u n +1 , Δ t ) . We de³ne the local truncation error (LTE = Δ t τ ) for the initial value problem ( ± ) by u (( n + 1) Δ t ) = u ( n Δ t ) + Δ t Φ( u ( n Δ t ) , u (( n + 1) Δ t ) , Δ t ) + Δ t τ where u is the exact solution of ( ± ). A onestep method is p th order accurate if the (global) error τ ∼ Δ t p ....
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 Fall '11
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 Numerical Analysis, Approximation, local truncation error, Theorem of Numerical Analysis

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