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This article is cited in 2 scientific papers (total in 2 papers)
Stability of a spline collocation difference scheme for a quasi-linear differential algebraic system of first-order partial differential equations
S. V. Svinina Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia
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.
Key words:
differential algebraic systems, partial differential equations, spline collocation method, difference scheme, matrix pencil.
Received: 30.05.2017
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
Linking options:
https://www.mathnet.ru/eng/zvmmf10856 https://www.mathnet.ru/eng/zvmmf/v58/i11/p1844
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Abstract page: | 211 | References: | 51 |
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