# This will involve the selection of an appropriate i

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern