On Taylor Model Based Integration of ODEs
نویسندگان
چکیده
منابع مشابه
On Taylor Model Based Integration of ODEs
The numerical solution of initial value problems (IVPs) for ODEs is one of the fundamental problems in computation. Today, there are many well-established algorithms for solving IVPs. However, traditional integration methods usually provide only approximate values for the solution. Precise error bounds are rarely available. The error estimates, which are sometimes delivered, are not guaranteed ...
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Since the early work of Moore, and perfected for the linear autonomous case by Lohner, it is known that preconditioning based on enclosing the accumulated errors in suitably chosen coordinate systems allows for effective suppression of the wrapping effect. The amount of error that needs to be accounted for itself can be significantly reduced by representing flows in terms of polynomials in the ...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2007
ISSN: 0036-1429,1095-7170
DOI: 10.1137/050638448