期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 52, 期 12, 页码 1695-1710出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2005.12.004
关键词
differential equations; Taylor approximations; a-priori error bounds; initial value problems; power series
This paper develops and demonstrates a guaranteed a-priori error bound for the Taylor polynomial approximation of any degree to the solution of initial value ordinary differential equations. The error bound is explicit and does not require upper bounds on the potentially complicated and intrinsically unknown right-hand side nor on any of its higher-order derivatives as with existing bounds, and thus it provides a valuable tool for the numerous applications in which initial value ode problems arise and for which approximate solutions must be sought. (c) 2006 Elsevier Ltd. All rights reserved.
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