Tài liệu Two Point Boundary Value Problems part 6 pptx

... North America). 17.5 Automated Allocation of Mesh Points In relaxation problems, you have to choose values for the independent variable at the mesh points. This is called allocating the grid or mesh. ... mesh. The usual procedure is to pick a plausible set of values and, if it works, to be content. If it doesn’t work, increasing the number of points usually cures the problem. If we know ahea...

Ngày tải lên: 21/01/2014, 18:20

... endpoints, others at interior (usually singular) points. The crucial distinction between initial value problems (Chapter 16) and two point boundary value problems (this chapter) is that in the former ... ,n 2 (17.0.3) There are two distinct classes of numerical methods for solving two point boundary value problems. In the shooting method (§17.1) we choose values for a...

Ngày tải lên: 24/12/2013, 12:16

... Output of sfroid mn c 2 λ exact λ sfroid 22 0. 16. 01427 6. 01427 1. 06. 14095 6. 14095 4. 06. 54250 6. 54253 25 1.030.4 361 30.4372 16. 0 36. 9 963 37.0135 411−1.0 131. 560 131.554 Shooting To solve the same problem ... vol. 151, pp. 351– 364 . [1] Keller, H.B. 1 968 , Numerical Methods for Two- Point Boundary- Value Problems (Waltham, MA: Blaisdell). Kippenhan, R., Weigert, A.,...

Ngày tải lên: 21/01/2014, 18:20

... uses (17.0.3) to convert an N-vector of ending values y(x 2 ) into an n 2 -vector of discrepancies F. 758 Chapter 17. Two Point Boundary Value Problems Sample page from NUMERICAL RECIPES IN C: ... 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 boundary value...

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 ... 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 ... singular point, if only because one has not usu...

Ngày tải lên: 24/12/2013, 12:16

... vol. 151, pp. 351– 364 . [1] Keller, H.B. 1 968 , Numerical Methods for Two- Point Boundary- Value Problems (Waltham, MA: Blaisdell). Kippenhan, R., Weigert, A., and Hofmeister, E. 1 968 , in Methods in ... are boundary value problems where even shooting to a fitting point fails — the integration interval has to be partitioned by several fitting points with the solution being ma...

Ngày tải lên: 24/12/2013, 12:16

... required to pass through zero at some unknown point x s .Weadd the equation z ≡ x s − x 1 dz dx =0 (17 .6. 3) 7 86 Chapter 17. Two Point Boundary Value Problems Sample page from NUMERICAL RECIPES ... 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 which a...

Ngày tải lên: 21/01/2014, 18:20

... extrapolated point and the average direction moved. Save the old starting point. ptt[j]=2.0*p[j]-pt[j]; xit[j]=p[j]-pt[j]; pt[j]=p[j]; } fptt=(*func)(ptt); Function value at extrapolated point. if ... direction u i and call this point P i . • For i =1, ,N −1,setu i ←u i+1 . • Set u N ← P N − P 0 . • Move P N to the minimum along direction u N and call this point P 0 . 4 16 Chapte...

Ngày tải lên: 15/12/2013, 04:15

Ngày tải lên: 23/12/2013, 11:15