Stability of a Spline Collocation Difference Scheme for a Quasi-Linear Differential Algebraic System of First-Order Partial Differential Equations


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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.

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S. Svinina

Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences

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