Difference methods for differential inclusions. (English) Zbl 0762.65042

Lempio, Frank

Modern methods of optimization, Proc. Summer Sch., Bayreuth/Ger. 1990, Lect. Notes Econ. Math. Syst. 378, 236-273 (1992).

[For the entire collection see Zbl 0746.00072.]
The study of differential inclusions is motivated by considering several model problems. The convergence proof for the linear multistep method for the initial value problem is outlined as the meaning of the corresponding assumptions is clarified. Finally, the ideas underlying the proof of higher order convergence results are presented.
By the way, the first order convergence of the Euler method under a one sided Lipschitz condition is proved. For the reader’s convenience, the results are illustrated by some numerical examples.

Reviewer: M.I.Krastanov (Sofia)

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L12	Finite difference and finite volume methods for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

difference methods; differential inclusions; convergence; linear multistep method; initial value problem; Euler method; numerical examples

Citations:

Zbl 0746.00072