Tài liệu Two Point Boundary Value Problems part 4 ppt

... Setuprowandcolumnmarkers. k2=m; nvars=ne*m; j1=1; j2=nb; j3=nb+1; j4=ne; j5=j4+j1; j6=j4+j2; j7=j4+j3; j8=j4+j4; j9=j8+j1; ic1=1; ic2=ne-nb; ic3=ic2+1; ic4=ne; jc1=1; jcf=ic3; for (it=1;it<=itmax;it++) { Primary iteration loop. k=k1; Boundary conditions ... are boundary value problems where even shooting to a fitting point fails — the integration interval has to be partitioned by...

Ngày tải lên: 24/12/2013, 12:16

... conditions are specified at endpoints, others at interior (usually singular) points. The crucial distinction between initial value problems (Chapter 16) and two point boundary value problems (this chapter) ... by far is where boundaryconditions are supposed to be satisfied at two points — usually the starting and ending values of the integration. However, the phrase two point...

Ngày tải lên: 24/12/2013, 12:16

... (17 .4. 12) y 2 = y  (17 .4. 13) y 3 = µ (17 .4. 14) Then y  1 = y 2 (17 .4. 15) y  2 = 1 1 − x 2  2x(m +1)y 2 −(y 3 −c 2 x 2 )y 1  (17 .4. 16) y  3 =0 (17 .4. 17) 780 Chapter 17. Two Point Boundary Value ... x k−1 ) 2 4 (17 .4. 25) β k = h 1 − 1 4 (x k + x k−1 ) 2 (17 .4. 26) Finally, equation (17 .4. 17) gives E 3,k = y 3,k − y 3,k−1 (17 .4. 27) 778 Chapter 17. Two Poi...

Ngày tải lên: 21/01/2014, 18:20

... 7 84 Chapter 17. Two Point Boundary Value Problems Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5) Copyright (C) 1988-1992 ... Handling Internal Boundary Conditions or Singular Points Singularities can occur in the interiors of two point boundaryvalue problems. Typically, there is a point x s at which a derivative must be eva...

Ngày tải lên: 21/01/2014, 18:20

... America). Keller, H.B. 1968, Numerical Methods for Two- Point Boundary- Value Problems (Waltham, MA: Blaisdell). 758 Chapter 17. Two Point Boundary Value Problems Sample page from NUMERICAL RECIPES IN ... n 2 for the partial derivatives. Each new cycle requires a new round of n 2 +1 integrations. This illustrates the enormous extra effort involved in solving two point b...

Ngày tải lên: 24/12/2013, 12:16

... 760 Chapter 17. Two Point Boundary Value Problems Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5) Copyright (C) 1988-1992 by ... f[]) Routine for use with newt to solve a two point boundary value problem for nvar coupled ODEs by shooting from x1 and x2 to a fitting point xf . Initial values for the nvar ODEs at x1 (x2) are ......

Ngày tải lên: 24/12/2013, 12:16

... block with only one equation: 7 84 Chapter 17. Two Point Boundary Value Problems Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5) Copyright (C) 1988-1992 ... Internal Boundary Conditions or Singular Points Singularities can occur in the interiors of two point boundary value problems. Typically, there is a point x s at whic...

Ngày tải lên: 21/01/2014, 18:20

... no. 1 4, pp. 225–231, 1995. 13 Y. An and R. Ma, “Global behavior of the components for the second order m -point boundary value problems, ” Boundary Value Problems, vol. 2008, Article ID 2 545 93, ... W 2  m e 2mt , W 3  4a 3  cos mt − sin mt  e mt , W 4  32m 6 . 2.16 From M ∈ 0,π 4 / 64 and m  √ 2/2 4 √ M, we have 0 <m<π /4, so W k > 0, k  1, 2, 3, 4...

Ngày tải lên: 21/06/2014, 16:20

... second-order two- point boundary value problems with nonlinearities across several eigenvalues. J. Appl. Math. Lett. 18, 587–595 (2005) [4] Rabinowitz, PH: Some global results for nonlinear eigenvalue problems. ... (HTML) versions will be made available soon. Nodal solutions of second-order two- point boundary value problems Boundary Value Problems 2012, 2012:13 doi:...

Ngày tải lên: 21/06/2014, 17:20

... Corporation Boundary Value Problems Volume 2007, Article ID 27621, 17 pages doi:10.1155/2007/27621 Research Article Solvability for a Class of Abstract Two- Point Boundary Value Problems Derived from ... −x 2 (t)   2 +   p 1 (t) −p 2 (t)   2 )dt +δc 1   x 1 (b) −x 2 (b)   2 . (4. 8) 16 Boundary Value Problems Remark 4. 5. Corollary 4. 4 improves the result [1...

Ngày tải lên: 21/06/2014, 22:20