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Monotone iterative method for differential equations with piecewise constant arguments. (English) Zbl 0978.65067

Periodic boundary value problems for differential equations with piecewise constant arguments are considered. Such equations are closely related to impulse and loaded equations and, especially, to difference equations of a discrete argument. They have the structure of continuous dynamical systems within intervals of certain length. The method of upper and lower solutions coupled with the monotone iterative technique is used to obtain existence and approximation results.
Reviewer: V.Arnăutu (Iaşi)

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37C27 Periodic orbits of vector fields and flows
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
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