Geodesic
On the recalculation of ellipsoids in estimating the error of~the~implicit Stormer method for a second-order linear~differential~equation
Vestnik rossijskih universitetov. Matematika, Tome 29 (2024) no. 148, pp. 391-400

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In the paper, a new method is proposed for constructing an error estimate for the numerical solution of the Cauchy problem for a second-order differential equation obtained using the implicit Stormer method. Unlike the previously proposed methods, it allows one to take into account the signs of small terms when recalculating ellipsoids containing the exact solution in the case of implicit multistep numerical method. This leads to a more accurate estimation of the error of the numerical solution and the applicability of the ellipsoid method over large intervals. A numerical experiment is presented demonstrating the effectiveness of the proposed method for obtaining a guaranteed error estimate of the implicit Stormer method.
Keywords: ellipsoid method, the Stormer method, numerical solution of the Cauchy problem for second-order ODEs
Mots-clés : error estimation 
@article{VTAMU_2024_29_148_a1,
     author = {N. D. Zolotareva},
     title = {On the recalculation of ellipsoids in estimating the error of~the~implicit {Stormer} method for a second-order linear~differential~equation},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {391--400},
     publisher = {mathdoc},
     volume = {29},
     number = {148},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2024_29_148_a1/}
}
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N. D. Zolotareva. On the recalculation of ellipsoids in estimating the error of~the~implicit Stormer method for a second-order linear~differential~equation. Vestnik rossijskih universitetov. Matematika, Tome 29 (2024) no. 148, pp. 391-400. http://geodesic.mathdoc.fr/item/VTAMU_2024_29_148_a1/