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# 24a 2 l 6 y1 x1 6 6 a6 6 6 3 i y2x2 i 6 4 yn

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Unformatted text preview: r ; RvN (b) ; 7 7 7 7 7 7 7 5 ; 7 7 7 7: 7 5 (7.2.4c) We will encounter algebraic systems like this in this and the following chapters. We'll describe procedures for solving them in Chapter 8 that only require O(N ) operations. 10 3. Once c has been determined, the BVP solution may be reconstructed from (7.2.3). Remark 1. All of the IVPs (7.2.2) can be solved in parallel on a computer with N processors. This is why multiple shooting is also called parallel shooting. Conte 5] described a method for stabilizing the procedure (7.1.7 - 7.1.10) which was later automated and improved by Scott and Watts 11]. The technique is less parallel than the one that we just described, but it does o er some advantages. To begin, we calculate solutions of the IVPs U1 = AU1 0 v1 = Av1 + b 0 x0 < x < x1 x0 < x x1 LU1 (a) = 0 Lv1(a) = l and write the solution of the BVP as y(x) = U1(x)c1 + v1 (x) As in Section 7.1, x0 < x < x1 : U1 = u(1) u(2) : : : u(1r) ]: 1 1 The integration proceeds to a point x1 where, due to the accumulation of round o errors, the columns of U1 no longer form a good linearly inde...
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