Numerical Methods for Nonlinear Variable Problems Episode 1 docx

... published in 19 84 ISBN 978-3-540-77506-5 DOI 10 .10 07/978-3-540-778 01- 1 e-ISBN 978-3-540-778 01- 1 Scientific Computation ISSN 14 34-8322 Library of Congress Control Number: 2007942575 © 2008, 19 84 Springer-Verlag ... seemed at first glance, for several reasons: 1. The first version of Numerical Methods for Nonlinear Variational Problems was, in fact, part of a set of m...

Ngày tải lên: 12/08/2014, 16:21

... = 1 in (2.9)). The proof of this regularity result will be given in the following simple case: L(v) = [ fv dx, f e L 2 (Q), (2 .10 ) T-OonQ. (2 .11 ) Before proving that (2 .10 ), (2 .11 ) ... - u) dx. (2 .16 ) By (2 .13 ) and (2 .16 ), we obtain E Vu £ • V(Au £ ) dx > s \ fAu s dx, so that, \u. • v(A«.) dx > f Au, dx. (2 .17 ) By Green's formula, (2 .17...

Ngày tải lên: 27/06/2014, 18:20

... examples 10 3 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 ... device 11 1 246 Starting methods 11 2 247 Numerical examples 11 3 25 Taylor Series Methods 11 4 250 Intr...

Ngày tải lên: 13/08/2014, 05:21

... = 1 in (2.9)). The proof of this regularity result will be given in the following simple case: L(v) = [ fv dx, f e L 2 (Q), (2 .10 ) T-OonQ. (2 .11 ) Before proving that (2 .10 ), (2 .11 ) ... in G.L.T. [1] , [2], [3]. For the approximation of the EVI of the first kind by finite element methods, we also refer the reader to Falk [1] , Strang [1] , Mosco and Strang [1] , Ciarl...

Ngày tải lên: 12/08/2014, 16:21

... {££ +1 , xt +i } from {u™ + *, \//% +1 }; in fact this is (5.88) with v/, = < +1 , <t> h = < +1 ; (ii) problem(5.99)toobtain{z^ +1 , ^ +1 }from{u^ +1 , ^ +1 },{^ +1 , ^ +1 }; (iii) ... (5 .10 1) T ™ +1 = 0™ +1 + y m +1 T^, (5 .10 2) m = m 4- 1 go to (5.96). It is clear that each iteration of algorithm (5.93)-(5 .10 2) requires the...

Ngày tải lên: 12/08/2014, 16:21

... obtain r" +1 = r"- p n Aw n . If r" +1 = 0, then x" + 1 = x = A" *b; if r" + * # 0, then compute x n +1 ,r" +1 ,g n +1 ,w n +1 by £& (42 91) (4.292) (4.293) g » +1 ... (4 .11 1) X satisfies (4.47), (4 .11 2) p e (L OO (Q)) /V , V • p = 0 (in the distribution sense). (4 .11 3) 348 App. I A Brief Introduction to Linear Variational...

Ngày tải lên: 12/08/2014, 16:21

... compli- cated problems (in fluid mechanics, semiconductor simulations, etc.). 6 Numerical Experiments 411 Figure 6 .13 . Triangulation 3~* (e = 1( T 3 , 8 = rc/3). Figure 6 .14 . Triangulation 9~\ (e = 10 " 5 , ... (4.209), (4. 310 ), respectively. We should easily prove that the approximate problem (4. 319 ) has a unique solution if (4. 311 )-(4. 313 ) hold. EXERCISE 4 .12 . Pro...

Ngày tải lên: 12/08/2014, 16:21

... 13 9, 14 0, 15 0, 15 2, 16 5, 16 6, 16 8, 17 0, 17 4, 17 6, 17 7, 17 8, 18 4, 18 5, 18 6, 18 7, 18 8, 19 1, 19 3, 19 4, 19 5, 208, 209, 211 , 214 , 219 , 2 21, 244, 245, 246, 248, 249, 250, 2 51, 253, 254, 259, 266, ... 98, 10 2, 10 4, 15 0, 17 0, 19 1, 19 4, 211 , 269, 292, 293, 444, 452 Varga, R. S. 41, 12 8, 14 0, 14 8, 15 8, 2 01, 384, 440, 452 Wags...

Ngày tải lên: 12/08/2014, 16:21

... y n 1 − 1 2 y 2 n 1 +1, y 0 =0, (13 4a) y n = y n 1 − 1 2 y 2 n 1 +1, y 0 =4, (13 4b) y n = y n 1 − y 2 n 1 +2,y 0 = 3 2 , (13 4c) y n = y n 1 2 + 1 y n 1 ,y 0 = 10 0, (13 4d) y n = y n 1 y n−2 +2 y n 1 + ... comprising (12 4d), (12 4e), (12 4f) has been reduced, first to an index 1 formulation (12 4d), (12 4e), (12 4h), and then to an ordinary differential equation system (1...

Ngày tải lên: 13/08/2014, 05:21

... is              000 − 529 3375 3904 3375 4232 3375 14 72 3375 18 9 92 00 15 2 25 − 12 7 25 − 419 10 0 − 11 18 575 3375 515 2 25 16 8 0 10 19 96 − 1 552 3375 515 2 25 16 8 0 10 19 96 − 1 552 000 10 00 0 01 0000 000 0 010              . For ... 10 −5 4.58854 82 8 −9 1. 02365 × 10 −5 4.78350 13 7 8 10 2 .15 123 × 10 −6 4.75845 228 8...

Ngày tải lên: 13/08/2014, 05:21