Geodesic
On the stability of a locally one-dimensional difference scheme for a first-order linear differential-algebraic system of index $(1,0)$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 37-50

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The 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 proved 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.
Keywords: differential-algebraic system, difference scheme, locally-one-dimensional method, index. 
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     author = {S. V. Svinina},
     title = {On the stability of a locally one-dimensional difference scheme for a first-order linear differential-algebraic system of index $(1,0)$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {37--50},
     publisher = {mathdoc},
     number = {4},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2023_4_a3/}
}
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S. V. Svinina. On the stability of a locally one-dimensional difference scheme for a first-order linear differential-algebraic system of index $(1,0)$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 37-50. http://geodesic.mathdoc.fr/item/IVM_2023_4_a3/