Tài liệu Partial Differential Equations part 3 pptx

... contrast, ψ n+1 j =(1+iH∆t) −1 ψ n j (19.2 .34 ) These are both first-order accurate in time, as can be seen by expanding equation (19.2 .32 ). However, neither operator in (19.2 .33 ) or (19.2 .34 ) is unitary. 19 .3 Initial Value ... Planck’s constant ¯h =1and the particle mass m =1/2.) One is given the initial wavepacket, ψ(x, t =0), together with boundary 852 Chapter 19. Partial Differ...

Ngày tải lên: 15/12/2013, 04:15

... U m (u n+(m−1)/m , ∆t) (19 .3. 20) 854 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright (C) 1988-1992 ... equation (19 .3. 3), we find ξ = 1 2 (cos k x ∆+cosk y ∆)− iα x sin k x ∆ − iα y sin k y ∆(19 .3. 6) where α x = v x ∆t ∆ ,α y = v y ∆t ∆ (19 .3. 7) 19 .3 Initial Value Problems in Mu...

Ngày tải lên: 15/12/2013, 04:15

... systems. In practice, equations (19.4 .33 ) should be rewritten to avoid numerical instabil- ity. For these and other practical details, refer to [2] . 860 Chapter 19. Partial Differential Equations Sample ... 862 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright (C) 1988-1992 by C...

Ngày tải lên: 15/12/2013, 04:15

... can only give a brief 868 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright (C) 1988-1992 by Cambridge ... equation Lu = ρ (19.5.1) 864 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright...

Ngày tải lên: 15/12/2013, 04:15

... free_dmatrix(irho[j],1,nn,1,nn); } free_dmatrix(irhs[1],1 ,3, 1 ,3) ; free_dmatrix(iu[1],1 ,3, 1 ,3) ; } 19.6 Multigrid Methods for Boundary Value Problems 8 83 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright ... 1-800-872-74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). CITED REFERENCES AND F...

Ngày tải lên: 24/12/2013, 12:16

... like this: f(x)=b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 + a 5 b 5 +··· (5.2.1) Printers prefer to write this as f(x)=b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 + a 5 b 5 + ··· (5.2.2) In either ... 5 .3 Polynomials and Rational Functions 1 73 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright (C) 1988-1992 ... without choos...

Ngày tải lên: 15/12/2013, 04:15

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