tailieunhanh - Burden - Numerical Analysis 5e (PWS, 1993) Episode 3 Part 6

Tham khảo tài liệu 'burden - numerical analysis 5e (pws, 1993) episode 3 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 618 CHAPTER 11 Boundary-Value Problems for Ordinary Differential Equations Table z Cf Xi ộ x Xxf - ỘOf 0 X 10 5 0 1 2 3 4 5 6 7 8 9 10 X 10 5 The hypotheses assumed at the beginning of this section are sufficient to guarantee that 1 2 Ộ x 2 dx f 0 i4 0 X 1. For a proof of this result see Schultz 131 pages 107-108. 5-splines can also be defined for unequally spaced nodes but the details are more complicated. A presentation of the technique can be found in Schultz 131 page 73. Another commonly used basis is the piecewise cubic Hermite polynomials. For an excellent presentation of this method again see Schultz 131 pages 24ff. Other methods that receive considerable attention are Galerkin or weak form methods. For the boundary-value problem we have been considering 7 ế q X y f x y ty y V ux dxỊ 0 X 1 under the assumptions listed at the beginning of this section the Galerkin and Rayleigh-Ritz methods are both determined by Eq. . This is not the case for an arbitrary boundary-value problem however. A treatment of the similarities and differences in the two methods and a discussion of the wide application of the Galerkin method can be found in Schultz 131 and in Strang and Fix 143 . Another popular technique for solving boundary-value problems is the method of 1 collocation. This procedure begins by selecting a set of basis functions ộỵ . . . ỘN a set of numbers x15. X in 0 1 and requiring that an approximation N 2 Ci f i x 1 satisfy the .

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