This will involve the selection of an appropriate i

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Unformatted text preview: est, we would control the error measure relative to the magnitude of the solution, e.g., ~ kdnk R kynk: It is also common to base an error test on a combination of an absolute and a relative tolerance, i.e., ~ kdnk R kynk + A: When some components of the solution are more important than others it may be appropriate to use a weighted norm with yi(t) in (3.5.6) replaced by yi(t)=wi, where w = w1 w2 : : : wm]T (3.5.7a) is a vector of positive weights. As an example, consider the weighted maximum norm of the local error estimate ~n ~ (3.5.7b) kdnkw = 1max dw i im i 1 ~ where dn i denotes the local error estimate of the i th component of dn . Use of a weighted test such as ~ kdnkw (3.5.7c) adds exibility to the software. Users may assign weights prior to the integration in proportion to the importance of a variable. The weighted norm may also be used to simulate a variety of standard tests. Thus, for example, an absolute error test would be obtained by setting wi = 1, i = 1 2 : : : m, and = A. A mixed error test where the integration step is accepted if the local error estimate of...
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This document was uploaded on 03/16/2014 for the course CSCI 6820 at Rensselaer Polytechnic Institute.

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