This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: q 11 =p 1 December 3, 2009 **F I NAL WILL BE T H URSDAY DECE MBER 17, 2009 at 5:30pm **REV IEW ON FR IDAY DECE MBER 11, 2009 at 2:00pm** Tentative** 2 nd order RungeKutta + = + xt Δt xt ΔtΦ = + Φ a1k1 a2k2 = ( , ) k1 f xt t = ( + , + ) k2 f xt q11k1Δt t p1Δt Parameters (the higher the order, the more parameters) a 1 , a 2 , … a n p 1 , p 2 , … p n q 11 Exact x(t+ Δ t) = +  + ! = (  ) + ! = (  ) … xτ xt dxdτtτ t 12 d2xdτ2τ t τ t 2 13 d3xdτ3τ t τ t 3 For = + τ t Δt + = + + ! = + ! = …; = ( , ) xt Δt xt dxdτtΔt 12 d2xdτ2τ tΔt2 13 d3xdτ3τ tΔt3 dxdτ f xτ τ = = = = d2xdτ2τ t ddτdxdtτ t , = ( ) + ddτfxτ τ dfdxτdx τ dτ dfdτx Aside: (Verifying ^ ^ ^) Let , = + fxτ τ 3sinx2τ 2τ = xτ 4τ2 Left hand side , = + ddτfxτ τ ddτ3 sin4τ22 2τ = + 3cos16τ464τ3 2 = + 192cos16τ4τ3 2 Right Hand Side = + dfdxτ 3cosx2τ2xτ 0 = + 3cosx22x8τ 2 = + 3cos4τ2224τ228τ 2 = + 192cos16τ4τ3 2 ( ) = + dx τ dτ 0 2 = dfdτx 8τ *E=Explicit Euler...
View
Full
Document
This note was uploaded on 01/08/2010 for the course COT 3502 taught by Professor Hawkins during the Fall '08 term at University of Florida.
 Fall '08
 Hawkins

Click to edit the document details