Numerical Methods for Ordinary Dierential Equations Episode 10 pot

... requirements. Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-72335-7 332 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL ... similar for backward difference methods and for Runge–Kutta and general linear methods that have a lower triangular coefficient matrix. For these simple methods...

Ngày tải lên: 13/08/2014, 05:21

... 60 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 10 0 10 −1 10 −2 10 −3 10 −4 10 −5 10 8 10 6 10 4 10 2 10 −0 10 −2 10 −4 n −1 E Figure 203(i) Norm error against n −1 for the ‘mildly ... can be 72 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 10 −5 10 −4 10 −3 10 −2 10 −1 10 −6 10 −5 10 −4 10 −3 10 −2 10 −...

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... the effect of the errors can be eliminated so that 202 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 10 2 10 3 10 4 10 −2 10 −6 10 10 number of f evaluations global error e =0.1 e =0.5 e ... 342(i). To turn this result into a recipe for constructing methods of order 2s we have: 224 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Table 344(I)...

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... examples 103 16 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS λ y 1 y 2 y 3 y λ x 0 0.2 0.5 1 2 5 10 20 50 10 2 10 3 10 4 0 10 −5 10 −4 10 −3 10 −2 10 −1 0.5 1.0 −0.0 10 4 −0.2 10 4 −0.4 10 4 −0.6 10 4 −0.8 10 4 −1.0 10 4 Figure ... k 2 y 3 +2k 3 y 2 )λ +2k 3 y 2 (k 1 + k 2 y 2 ). (104 i) xiv NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUA...

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... + Cθ 2 (θ−1)(θ−2) θ n ,θ=1,θ=2. 32 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 0 1 2 3 4 √ 2 1+ √ 2 2 √ 2 2+ √ 2 1+2 √ 2 10 10 2 1 Figure 121(ii) Solution to neutral delay differential equation (121c) the formula for ... these assumptions, the equations of motion become 38 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 13 Difference Equation Problems...

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... half-plane. 104 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 2 3 4 5 10 −4 10 −3 10 −2 10 −4 10 −6 10 −8 10 10 h E Figure 239(ii) Runge–Kutta methods with cost corrections methods. However, for ... implicit method (237a). NUMERICAL DIFFERENTIAL EQUATION METHODS 103 2 3 4 5 10 −4 10 −3 10 −2 10 −4 10 −6 10 −8 10 10 h E Figure 239...

Ngày tải lên: 13/08/2014, 05:21

... variable step method discussed in Exercise 27.2. NUMERICAL DIFFERENTIAL EQUATION METHODS 127 10 −3 10 −2 10 −1 10 −2 10 −4 10 −6 10 −8 10 10 10 −12 h E Pseudo Runge–Kutta method Runge–Kutta ... labelled by Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-72335-7 158 NUMERICA...

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... Φ(t)=1/γ(t)is satisfied for trees t =[τ k−1 [τ l−1 ]] for k ≤ η and l ≤ ζ.Thisisanecessary condition for orders at least η + ζ. 188 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Again we see ... = 1 p! . (324h) 170 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 32 Low Order Explicit Methods 320 Methods of orders less than 4 It will be shown in Subse...

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... P k−1 (v) is √ 2k −1  2k−2 k−1  , with a similar formula for the leading coefficient of P k (u). 240 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS The fact that D s (z) cannot vanish now ... Vandermonde matrix V =  1 cc 2 ··· c s−1  , 256 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Lemma 359A Let X G = W BAW, where A and B =diag(b) are as for the Ga...

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... −b s 280 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 38 Algebraic Properties of Runge–Kutta Methods 380 Motivation For any specific N-dimensional initial value problem, Runge–Kutta methods can ... acceptable for many problems. In each of the values of ξ for which there is a single underline, the method is A(α)-stable with α ≥ 1.55 ≈ 89 ◦ . 272 NUMERICAL METHODS...

Ngày tải lên: 13/08/2014, 05:21