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N. Zolotareva (2005)
A Guaranteed Error Estimate for the Stormer Method on Large IntervalsDifferential Equations, 41
ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 7, pp. 950–958. c Pleiades Publishing, Ltd., 2007. Original Russian Text c N.D. Zolotareva, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 7, pp. 929–937. NUMERICAL METHODS. FINITE-DIFFERENCE EQUATIONS On the Derivation of Guaranteed Error Estimates for the Adams Method N. D. Zolotareva Moscow State University, Moscow, Russia Received October 12, 2006 DOI: 10.1134/S0012266107070087 1. INTRODUCTION Methods for estimating the error in the numerical solution v of the problem x = f (t, x),x(0) = x,x,f ∈ R , 0 ≤ t ≤ T , 0 0 by the kth-order Adams method k−1 ∇v = hf (t ,v ) − h β ∇ f (t ,v )+ w ,k − 1 ≤ m ≤ M, (1) m m m i+1 m m m i=1 were described in [1, 2]. Here k ≥ 2; t = lh, l =0, 1, 2,... ; w is the vector of roundoff errors at the mth step; β are the coefficients of the Adams method m i [3, p. 334]. The error estimate methods suggested in [1, 2] are based on the use of ellipsoids [4]. The ellipsoid 1/2 E(0,B) was defined as
Differential Equations – Springer Journals
Published: Oct 2, 2007
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