ISSN:
0945-3245
Keywords:
AMS(MOS): 65L05
;
CR: G1.7
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary We consider minimal-error algorithms for solving systems of ODE, $$z'\left( t \right) = f\left( {t, z\left( t \right)} \right),z\left( 0 \right) = z_0 ,where f:\left[ {0, c} \right] \times \mathbb{R}^s \to \mathbb{R}^s $$ . We show how to increase the order of an algorithm by one, using additionally integrals off. We define the Taylor-integral algorithm which has the error of ordern −(r+1) which is minimal among all algorithms which usen linear or nonlinear smooth functionals off, in the class of bounded functionsf with bounded partial derivatives up to orderr. We show that the Taylor algorithm has the error of ordern −r which is minimal among all algorithms which usen evaluations off and/or its partial derivatives.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01379663
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