Abstract:
A quasi-linear differential algebraic system of partial differential equations with a special structure of the pencil of Jacobian matrices of small index is considered. A nonlinear spline collocation difference scheme of high approximation order is constructed for the system by approximating the required solution by a spline of arbitrary in each independent variable. It is proved by the simple iteration method that the nonlinear difference scheme has a solution that is uniformly bounded in the grid space. Numerical results are demonstrated using a test example.
Citation:
S. V. Svinina, “Stability of a spline collocation difference scheme for a quasi-linear differential algebraic system of first-order partial differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018), 1844–1862; Comput. Math. Math. Phys., 58:11 (2018), 1775–1791
\Bibitem{Svi18}
\by S.~V.~Svinina
\paper Stability of a spline collocation difference scheme for a quasi-linear differential algebraic system of first-order partial differential equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 11
\pages 1844--1862
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\crossref{https://doi.org/10.31857/S004446690003537-1}
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\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 11
\pages 1775--1791
\crossref{https://doi.org/10.1134/S0965542518110131}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10856
https://www.mathnet.ru/eng/zvmmf/v58/i11/p1844
This publication is cited in the following 2 articles:
S. V. Svinina, “On conditions for the absolute stability of one difference scheme for some multidimensional differential-algebraic systems”, Russian Math. (Iz. VUZ), 66:8 (2022), 56–65
S. V. Svinina, “On a quasi-linear partial differential algebraic system of equations”, Comput. Math. Math. Phys., 59:11 (2019), 1791–1805
Citation in format AMSBIB
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