BSU bulletin. Mathematics, Informatics
ABOUT COLLOCATION-VARIATIONAL DIFFERENCE SCHEME FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS // BSU bulletin. Mathematics, Informatics. - 2017. №3. . - С. 3-9.
ABOUT COLLOCATION-VARIATIONAL DIFFERENCE SCHEME FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS
The article deals with the systems of ordinary differential equations with an identically degenerate matrix preceding a derivative (differential-algebraic equations). The initial condition is supposed to be consistent with the right- hand side, so the problem under consideration has a solution. We have given necessary definitions from the theory of solving differential-algebraic and stiff ordinary differential equations and shown the difficulties of their numerical solution. A special case of the collocation-variational method for solving differential-algebraic equations containing stiff components and having index not exceeding two is considered. We have obtained the stabil- ity functions for the Dahlquist model equation, and made numerical calcula- tions of the known test examples.
differential-algebraic equations; difference schemes; index; stiff problems; A-stability; stability functions.
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