Abstract
A class (m,k)-methods is discussed for the numerical solution of the initial value problems for implicit systems of ordinary differential equations. The order conditions and convergence of the numerical solution in the case of implementation of the scheme with the time-lagging of matrices derivatives for systems of index 1 are obtained. At \(k\le 4\) the order conditions are studied and schemes optimal computing costs are obtained.
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Levykin, A.I., Novikov, E.A. (2015). A Study of (m,k)-Methods for Solving Differential-Algebraic Systems of Index 1. In: Danaev, N., Shokin, Y., Darkhan, AZ. (eds) Mathematical Modeling of Technological Processes. CITech 2015. Communications in Computer and Information Science, vol 549. Springer, Cham. https://doi.org/10.1007/978-3-319-25058-8_10
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DOI: https://doi.org/10.1007/978-3-319-25058-8_10
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