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On the Stability of Spline Collocation Difference Scheme for Linear Multidimensional Differential-Algebraic Systems

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Abstract

An initial-boundary value problem is considered for a linear multidimensional differential-algebraic system of first-order equations with variable matrix coefficients of a special form. A spline collocation method is used to solve it numerically. Unlike splitting methods, this method allows taking into account the structural features of all matrix coefficients of the system in total and has a high accuracy, which coincides with the order of the multidimensional approximating spline. A multidimensional spline collocation difference scheme is presented. A theorem on the stability of the difference scheme under certain conditions on the matrix coefficients of the system is proved. Finally, the results of numerical calculations for the test example are given.

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Funding

This work is supported by the Ministry of Science and Higher Education of the Russian Federation within the “Theory and methods of studying evolution equations and controlled systems with their applications” base project no. 121041300060-4.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Science, 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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Translated by M. Talacheva

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Svinina, S.V. On the Stability of Spline Collocation Difference Scheme for Linear Multidimensional Differential-Algebraic Systems. Russ Math. 66, 56–65 (2022). https://doi.org/10.3103/S1066369X22080096

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  • DOI: https://doi.org/10.3103/S1066369X22080096

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