On the convergence of multistep methods for ordinary differential equations with discontinuities. (English) Zbl 0571.65065

Jankowski, Tadeusz

Demonstr. Math. 16, 651-675 (1983).

This paper is concerned with the solution of an initial value problem on some interval, where the solution satisfies the initial condition and the differential equation almost everywhere on that interval, by quasilinear multistep methods. (Such methods include the family of linear multistep methods as a special case.) Sufficient conditions for the convergence of this class of methods are given, relating convergence to the concepts of consistency and stability in the usual way. The order and stability and convergence of a subclass of this family of methods is studied.

Reviewer: K.Burrage

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

quasilinear multistep methods; convergence; consistency