On the Stability of Some Spline Collocation Implicit Difference Scheme

TL;DR

This paper develops a spline collocation difference scheme for linear partial differential algebraic equations with multiple characteristics, establishing conditions for its absolute stability.

Contribution

It introduces a new spline collocation difference scheme of arbitrary degree and derives sufficient stability conditions for systems with multiple characteristic curves.

Findings

Constructed a difference scheme of arbitrary degree using spline collocation.

Derived sufficient conditions for the scheme's absolute stability.

Applied the method to systems with multiple characteristic curves.

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.