On the Stability of Some Spline Collocation Implicit Difference Scheme

Abstract

Boundary problem for linear partial differential algebraic equations system with multiple characteristic curves is considered. It is supposed that matrix-functions pencil of the system under consideration is smoothly equivalent to special canonical form. For this problem, with the help of the spline collocation method, a difference scheme of arbitrary degree of approximation with respect to each variable is constructed. Sufficient conditions for its absolute stability is found.