Numerical Methods for Ordinary Dierential Equations Episode 11 pptx

... equation for the error in step n, which will be written as  n = y(x n ) −y n ,intheform  n − k  i=1 α i  n−i = Kh p+1 , 362 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS For U ∈ R kN ,writeU i , ... y n ). (452c) 350 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 1 2 3 1 2 i −i −2 −1 0 Figure 434(i) Stability regions for Adams–Moulton methods (s...

Ngày tải lên: 13/08/2014, 05:21

... gives   AU BV   =                5 33 0 19 11 − 8 11 − 1 66 4 11 19 22 4753 7920 251 1440 19 11 − 8 11 − 449 15840 3463 7920 449 660 5 33 0 19 11 − 8 11 − 1 66 4 11 19 22 4753 7920 251 1440 19 11 − 8 11 − 449 15840 3463 7920 449 660 00 ... MULTISTEP METHODS 369 Table 461(I) Coefficients, γ 0 , γ 1 , , γ p , for Nordsieck methods p =2 p =3 p =4 p =5 p...

Ngày tải lên: 13/08/2014, 05:21

... 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 ... General form of linear multistep methods 107 243 Consistency, stability and convergence 107 244 Predictor–corrector Adams methods 109 245 The Milne device 111 246 Star...

Ngày tải lên: 13/08/2014, 05:21

... C 2 (x)Y (m−2) (x) −···−C m (x)Y (x)=g(x). (111 c) 22 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 10.3 The matrix A =(N −1) 2              110 ··· 000 1 −21··· 000 01−2 ··· 000 . . . . . . . . . . . . . . . . . . 000··· ... these assumptions, the equations of motion become 38 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 13 Difference Equa...

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... value. 62 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 0123 0.05 0.10 0.15 x h Figure 203(iii) Stepsize h against x for the ‘mildly stiff’ problem (203a) with variable stepsize for T =0.02 The ... This is done by writing Φ(ξ, x) for the solution at x to the differential equation w  (x)= ∂f ∂y w(x),w(ξ)=I, 66 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATION...

Ngày tải lên: 13/08/2014, 05:21

... 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 methods k β 1 β 2 β 3 β 4 β 5 β 6 β 7 β 8 C 1 ... 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...

Ngày tải lên: 13/08/2014, 05:21

... 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...

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...

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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 ... values of the 198 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 33 Runge–Kutta Methods with Error Estimates 330 Introduction Practical computations w...

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 ... rearrange to deduce (357e).  234 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Table 352(I) Pad´e approximations N lm /D lm for l, m =0, 1, 2, 3   l m 01 2 3 0...

Ngày tải lên: 13/08/2014, 05:21