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 −...

Ngày tải lên: 13/08/2014, 05:21

... 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)...

Ngày tải lên: 13/08/2014, 05:21

... 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...

Ngày tải lên: 13/08/2014, 05:21

... 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...

Ngày tải lên: 13/08/2014, 05:21

... 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...

Ngày tải lên: 13/08/2014, 05:21

... −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