Tài liệu Partial Differential Equations part 4 ppt

... Um(un+(m−1)/m, ∆t)(19.3.20)8 54 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 ... 856Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 by Cambridge ... AND FURTHER READING:Ames, W.F. 1977,Numerical Methods for Partial Differential Equations , 2nd ed. (New York:Academic Press).19 .4 Fourier and Cyclic Reduction Methods forBoundary Value ProblemsAs...

Tài liệu Partial Differential Equations part 3 pptx

... 848 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 ... Planck’s constant ¯h =1and the particle massm =1/2.) One is given the initial wavepacket, ψ(x, t =0), together with boundary852Chapter 19. Partial Differential Equations Sample page from NUMERICAL ... high-order method you850Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 by Cambridge...

Tài liệu Partial Differential Equations part 5 ppt

... systems.In practice, equations (19 .4. 33) should be rewritten to avoid numerical instabil-ity. For these and other practical details, refer to[2].860Chapter 19. Partial Differential Equations Sample ... Similarly,ρjl=1JLJ−1m=0L−1n=0ρmne−2πijm/Je−2πiln/L(19 .4. 3)If we substitute expressions (19 .4. 2) and (19 .4. 3) in our model problem (19.0.6),we ﬁndumne2πim/J+ e−2πim/J+ e2πin/L+ e−2πin/L− 4 =ρmn∆2(19 .4. 4)orumn=ρmn∆22cos2πmJ+cos2πnL− ... equation (19 .4. 24) givesuB−1,l= −2∆gl(19 .4. 25)All the uBterms in equation (19 .4. 19) vanish except when j =0:u1,l+ u−1,l+ u0,l+1+ u0,l−1− 4u0,l=2∆gl+∆2ρ0,l(19 .4. 26)Thus...

Tài liệu Partial Differential Equations part 6 doc

... elliptic equationLu = ρ (19.5.1)8 64 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 ... can only give a brief868Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 by Cambridge ... ∆t/∆2≤1 4 . Suppose we try to takethe largest possible timestep, and set ∆t =∆2 /4. Then equation (19.5 .4) becomesun+1j,l=1 4 unj+1,l+ unj−1,l+ unj,l+1+ unj,l−1−∆2 4 ρj,l(19.5.5)Thus...

Tài liệu Partial Differential Equations part 7 doc

... (19.6 .45 )Since∂L∂ui,j= 4/ h2+2ui,j(19.6 .46 )the Newton Gauss-Seidel iteration isunewi,j= ui,j−L(ui,j) 4/ h2+2ui,j(19.6 .47 )Here is a routine mgfasthat solves equation (19.6 .44 ) ... starLh=1h20101 41 010(19.6.19)888Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright ... Multigrid Methods(New York: Wiley).8 84 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992...

Tài liệu Integration of Ordinary Differential Equations part 4 ppt

... implement (16.3 .4) , since we will soon do even better.Now would be a good time to look back at the routine qsimp in 4. 2, andespecially to compare equation (4. 2 .4) with equation (16.3 .4) above. You ... most important application as a part ofthe more powerful Bulirsch-Stoer technique, treated in §16 .4. You can thereforeconsider this section as a preamble to §16 .4. The number of right-hand side ... estimatey(x + H) ≈4yn− yn/23(16.3 .4) is fourth-order accurate, the same as fourth-order Runge-Kutta, but requires onlyabout 1.5 derivative evaluations per step h instead of Runge-Kutta’s 4 evaluations.Don’t...

Tài liệu Insight into IELTS part 4 pptx

... antibioticsfrom microbes found eitherinside the intestines of theamber-encased insects or in soilparticles trapped with themwhen they were caught bysticky tree resin up to 130million years ago. ... to find out how (3) the antibiotics will be.Microbes that seem to have the characteristics of (4) diseases will haveto be killed.It is thought that a (5) molecule could lead to a whole series ... achievement.It is necessary to be (8) about maintaining the life of the antibiotics.Reading UNIT 4 D The wind farm is connected to thepower station by a 33-kilovoltpowerline, and a radio link...

15
1,854
9

Tài liệu Bullentin for toefl part 4 pptx

... ServicePO Box 6151Princeton, NJ 08 541 -6151 USAChecks must be made payable to ETS-TOEFL/TSE. In Canada, add GST/HST (Reg. No. 13 141 446 8 RT)and QST (Reg. No. 1087967 545 ) to total remittance. It is ... for department name blank• write 00 in the boxes for department codeIf you plan to study at the graduate level• look at the Department Code list in the Bulletin• find the name of the department ... Make remittance payable to ETS-TOEFL/TSE. In Canada, add GST/HST (Reg. No. 13 141 446 8 RT) and QST (Reg. No. 1087967 545 ) to total remittance. It is not necessary to add VAT for TOEFL/TSE fees and...

Tài liệu Modeling of Data part 4 pptx

... vol. 86, pp. 149 –155; see also vol. 95, p. 1300(1988). [3]Lybanon, M. 19 84, American Journal of Physics, vol. 52, pp. 22–26. [4] York, D. 1966,Canadian Journal of Physics, vol. 44 , pp. 1079–1086. ... ﬁt.}fit(xx,yy,nn,ww,1,&dum1,b,&dum2,&dum3,&dum4,&dum5); Trial ﬁt for b.offs=ang[1]=0.0; Construct several angles for refer-ence points, and make b an an-gle.ang[2]=atan(*b);ang [4] =0.0;ang[5]=ang[2];ang[6]=POTN;for (j =4; j<=6;j++) ... swap,amx,amn,varx,vary,ang[7],ch[7],scale,bmn,bmx,d1,d2,r2,dum1,dum2,dum3,dum4,dum5;xx=vector(1,ndat);yy=vector(1,ndat);670Chapter 15. Modeling of DataSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright...

Tài liệu Evaluation of Functions part 4 pptx

... (5.3.2)where A, B, C, D, and E are to be precomputed byA =(a 4 )1 /4 B=a3−A34A3D=3B2+8B3+a1A−2a2BA2C =a2A2−2B−6B2−DE =a0−B 4 −B2(C+D)−CD(5.3.3) ... an extra addition.For example, the polynomialP (x)=a0+a1x+a2x2+a3x3+a 4 x 4 (5.3.1)where a 4 > 0, can be evaluated with 3 multiplications and 5 additions as follows:P (x)=[(Ax ... Applied Mathematics, vol. 23, pp. 165–179. [4] Kronsj¨o, L. 1987,Algorithms: Their Complexity and Efﬁciency, 2nd ed. (New York: Wiley). [5]5 .4 Complex ArithmeticAs we mentioned in §1.2,...

Xem thêm