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December 1

# December 1 - December 1 2009 The lectures correspond with...

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+ = + xt Δt xt Δt x t t + Δ t December 1, 2009 The lectures correspond with Chapter 25 The book uses dydx lectures use dxdt both are the same Algebraic Equations F(x) = 0 Special Case Linear – if linear then you can use A -1 = - fx Ax b - = → = Ax b 0 Ax b = - x A 1b The result is then numerical If non-linear Use Newton-Raphson Ordinary Differential Equations = ( ) dxdt f xtt = = ( ) soln x x t Special Case: Linear = + fxtt Axt bt = + x Ax bt = ( ) xt Wz t Numerical - Explicit Euler - Implicit Euler - Heun (Luke) - Modified(Stephanie) - 2 nd Order RK - 4 th Order RK Explicit Euler + = + ( ) xpt Δt xt Δtf xtt The correct version to use is + = + , + + , + xt Δt xt Δtfxt t fxpt Δt t Δt2 When using + = + ( ) xpt Δt2 xt Δt2f xtt The correct version to use is

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December 1, 2009 + = + + , + xt Δt xt Δtfxpt Δt2 t Δt2
December 1, 2009 NOT EXPLAINED IN TEXT BOOK Runge-Kutta Method Concept -trying to get from time t to time Δ t Predicted slope -weighted average of different predicted slopes

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December 1 - December 1 2009 The lectures correspond with...

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