Unformatted text preview: r ; RvN (b)
5 ; 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 )
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 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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- Spring '14
- Boundary value problem, BVPs