Numerical Methods for Ordinary Dierential Equations Episode 14 pdf

... Hybrid methods for initial value problems in ordinary differential equations. SIAM J. Numer. Anal., 2, 69–86. 450 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 558 Scale and modify for error ... 24 Lotka–Volterra, 18 Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-72335-7...

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... k 2 y 3 +2k 3 y 2 )λ +2k 3 y 2 (k 1 + k 2 y 2 ). (104i) xiv NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS problems. For implicit methods for stiff problems, inexpensive implementation costs must ... and modify for error estimation 450 References 453 Index 459 14 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Given that consistent initial values are...

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... these assumptions, the equations of motion become 38 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 13 Difference Equation Problems 130 Introduction to difference equations While differential equations ... k<1, such that, for any η, ζ ∈ M, ρ(φ(η),φ(ζ)) ≤ kρ(η, ζ). Then there exists a unique ξ ∈ M such that φ(ξ)=ξ. 46 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL...

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... 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 −1 h |E| x = 1 2 x =1 Figure 214( ii) Error versus stepsize for problem (214c) ... does 70 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 10 −5 10 −4 10 −3 10 −2 10 −1 10 −10 10 −8 10 −6 10 −4 10 −2 h |E| x =1.29 x = π 4 Figure 214( i) Error versus...

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... vertex of the tree. For 106 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS of order. However, the conclusion turns out to be exactly the same as for Adams–Bashforth methods: if every term ... 201, y  (x)= y + x y −x ,y(0) = 1. (252a) 110 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Table 244(I) Coefficients and error constants for Adams–Bashforth met...

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... 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 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL ... abnormally short. Consider, for example, the two-dimensional problem 152 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Table 310(II) Elementary differe...

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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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... 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) Methods in the Radau and Lobatto families Name ... as we 214 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 341 Solvability of implicit equations As we have remarked, explicit evaluation of the stage...

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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