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On the Stability of a Locally One-Dimensional Difference Scheme for a First-Order Linear Differential-Algebraic System of Index (1, 0)

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Abstract

This paper considers an initial-boundary value problem for a linear multidimensional first-order differential-algebraic system of index (1, 0). For its numerical solution, a four-point three-layer locally one-dimensional difference scheme is used. It is proven that, under certain conditions on the steps of the difference grid, such a scheme is stable in terms of the initial-boundary conditions and in the right-hand side. The results of numerical experiments are presented.

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Funding

This work was carried out as part of the basic project “Theory and Methods for Studying Evolutionary Equations and Control Systems with Their Applications,” no. 121041300060-4.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia

    S. V. Svinina

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  1. S. V. Svinina
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Correspondence to S. V. Svinina.

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Svinina, S.V. On the Stability of a Locally One-Dimensional Difference Scheme for a First-Order Linear Differential-Algebraic System of Index (1, 0). Russ Math. 67, 31–43 (2023). https://doi.org/10.3103/S1066369X23040059

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